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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he" class=""><span>תרומה לוויקיפדיה</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9E%D7%A8%D7%97%D7%91+%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת" class=""><span>יצירת חשבון</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9E%D7%A8%D7%97%D7%91+%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o" class=""><span>כניסה לחשבון</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="אפשרויות נוספות" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="כלים אישיים" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9E%D7%A8%D7%97%D7%91+%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>יצירת חשבון</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%9E%D7%A8%D7%97%D7%91+%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>כניסה לחשבון</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> דפים לעורכים שלא נכנסו לחשבון <a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A8%D7%95%D7%9B%D7%99%D7%9D_%D7%94%D7%91%D7%90%D7%99%D7%9D" aria-label="מידע נוסף על עריכה"><span>מידע נוסף</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%AA%D7%A8%D7%95%D7%9E%D7%95%D7%AA_%D7%A9%D7%9C%D7%99" title="רשימת העריכות שנעשו מכתובת IP זו [y]" accesskey="y"><span>תרומות</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A9%D7%99%D7%97%D7%94_%D7%A9%D7%9C%D7%99" title="דיון על העריכות שנעשו מכתובת IP זו [n]" accesskey="n"><span>שיחה</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"><div id="mw-dismissablenotice-anonplace"></div><script>(function(){var node=document.getElementById("mw-dismissablenotice-anonplace");if(node){node.outerHTML="\u003Cdiv class=\"mw-dismissable-notice\"\u003E\u003Cdiv class=\"mw-dismissable-notice-close\"\u003E[\u003Ca tabindex=\"0\" role=\"button\"\u003Eהסתרה\u003C/a\u003E]\u003C/div\u003E\u003Cdiv class=\"mw-dismissable-notice-body\"\u003E\u003C!-- CentralNotice --\u003E\u003Cdiv id=\"localNotice\" data-nosnippet=\"\"\u003E\u003Cdiv class=\"anonnotice\" lang=\"he\" 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class="vector-main-menu-landmark" aria-label="אתר"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="תוכן עניינים" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">תוכן עניינים</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">הסתרה</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">התחלה</div> </a> </li> <li id="toc-הגדרה" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#הגדרה"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>הגדרה</span> </div> </a> <ul id="toc-הגדרה-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-המרחב_L2" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#המרחב_L2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>המרחב <i>L<sup>2</sup></i></span> </div> </a> <ul id="toc-המרחב_L2-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-דוגמאות_נוספות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#דוגמאות_נוספות"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>דוגמאות נוספות</span> </div> </a> <ul id="toc-דוגמאות_נוספות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-בניות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#בניות"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>בניות</span> </div> </a> <button aria-controls="toc-בניות-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>שינוי מצב התת־פרק בניות</span> </button> <ul id="toc-בניות-sublist" class="vector-toc-list"> <li id="toc-סכום_ישר_של_מרחבי_הילברט" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#סכום_ישר_של_מרחבי_הילברט"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>סכום ישר של מרחבי הילברט</span> </div> </a> <ul id="toc-סכום_ישר_של_מרחבי_הילברט-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-מנה_של_מרחבי_הילברט" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#מנה_של_מרחבי_הילברט"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>מנה של מרחבי הילברט</span> </div> </a> <ul id="toc-מנה_של_מרחבי_הילברט-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-ראו_גם" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#ראו_גם"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>ראו גם</span> </div> </a> <ul id="toc-ראו_גם-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-קישורים_חיצוניים" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#קישורים_חיצוניים"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>קישורים חיצוניים</span> </div> </a> <button aria-controls="toc-קישורים_חיצוניים-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>שינוי מצב התת־פרק קישורים חיצוניים</span> </button> <ul id="toc-קישורים_חיצוניים-sublist" class="vector-toc-list"> <li id="toc-עץ_מיון_של_מרחבים_וקטוריים_טופולוגיים" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#עץ_מיון_של_מרחבים_וקטוריים_טופולוגיים"> <div class="vector-toc-text"> <span class="vector-toc-numb">6.1</span> <span>עץ מיון של מרחבים וקטוריים טופולוגיים</span> </div> </a> <ul id="toc-עץ_מיון_של_מרחבים_וקטוריים_טופולוגיים-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="תוכן עניינים" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="מצב תוכן העניינים" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">מצב תוכן העניינים</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">מרחב הילברט</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="מעבר לערך בשפה אחרת. זמין ב־59 שפות" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-59" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">59 שפות</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en badge-Q17437798 badge-goodarticle mw-list-item" title="ערך טוב"><a href="https://en.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – אנגלית" lang="en" hreflang="en" data-title="Hilbert space" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Hilbert-ruimte" title="Hilbert-ruimte – אפריקאנס" lang="af" hreflang="af" data-title="Hilbert-ruimte" data-language-autonym="Afrikaans" data-language-local-name="אפריקאנס" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%D8%A1_%D9%87%D9%8A%D9%84%D8%A8%D8%B1%D8%AA" title="فضاء هيلبرت – ערבית" lang="ar" hreflang="ar" data-title="فضاء هيلبرت" data-language-autonym="العربية" data-language-local-name="ערבית" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Espaciu_de_Hilbert" title="Espaciu de Hilbert – אסטורית" lang="ast" hreflang="ast" data-title="Espaciu de Hilbert" data-language-autonym="Asturianu" data-language-local-name="אסטורית" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Hilbert_f%C9%99zas%C4%B1" title="Hilbert fəzası – אזרית" lang="az" hreflang="az" data-title="Hilbert fəzası" data-language-autonym="Azərbaycanca" data-language-local-name="אזרית" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82_%D0%B0%D1%80%D0%B0%D1%83%D1%8B%D2%93%D1%8B" title="Гильберт арауығы – בשקירית" lang="ba" hreflang="ba" data-title="Гильберт арауығы" data-language-autonym="Башҡортса" data-language-local-name="בשקירית" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Хилбертово пространство – בולגרית" lang="bg" hreflang="bg" data-title="Хилбертово пространство" data-language-autonym="Български" data-language-local-name="בולגרית" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B9%E0%A6%BF%E0%A6%B2%E0%A6%AC%E0%A6%BE%E0%A6%B0%E0%A7%8D%E0%A6%9F_%E0%A6%9C%E0%A6%97%E0%A7%8E" title="হিলবার্ট জগৎ – בנגלית" lang="bn" hreflang="bn" data-title="হিলবার্ট জগৎ" data-language-autonym="বাংলা" data-language-local-name="בנגלית" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Espai_de_Hilbert" title="Espai de Hilbert – קטלאנית" lang="ca" hreflang="ca" data-title="Espai de Hilbert" data-language-autonym="Català" data-language-local-name="קטלאנית" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DB%86%D8%B4%D8%A7%DB%8C%DB%8C%DB%8C_%DA%BE%DB%8C%D9%84%D8%A8%DB%8E%D8%B1%D8%AA" title="بۆشاییی ھیلبێرت – כורדית סוראנית" lang="ckb" hreflang="ckb" data-title="بۆشاییی ھیلبێرت" data-language-autonym="کوردی" data-language-local-name="כורדית סוראנית" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Hilbert%C5%AFv_prostor" title="Hilbertův prostor – צ׳כית" lang="cs" hreflang="cs" data-title="Hilbertův prostor" data-language-autonym="Čeština" data-language-local-name="צ׳כית" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Hilbertrum" title="Hilbertrum – דנית" lang="da" hreflang="da" data-title="Hilbertrum" data-language-autonym="Dansk" data-language-local-name="דנית" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Hilbertraum" title="Hilbertraum – גרמנית" lang="de" hreflang="de" data-title="Hilbertraum" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CF%8E%CF%81%CE%BF%CF%82_%CE%A7%CE%AF%CE%BB%CE%BC%CF%80%CE%B5%CF%81%CF%84" title="Χώρος Χίλμπερτ – יוונית" lang="el" hreflang="el" data-title="Χώρος Χίλμπερτ" data-language-autonym="Ελληνικά" data-language-local-name="יוונית" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Hilberta_spaco" title="Hilberta spaco – אספרנטו" lang="eo" hreflang="eo" data-title="Hilberta spaco" data-language-autonym="Esperanto" data-language-local-name="אספרנטו" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Espacio_de_Hilbert" title="Espacio de Hilbert – ספרדית" lang="es" hreflang="es" data-title="Espacio de Hilbert" data-language-autonym="Español" data-language-local-name="ספרדית" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Hilberti_ruum" title="Hilberti ruum – אסטונית" lang="et" hreflang="et" data-title="Hilberti ruum" data-language-autonym="Eesti" data-language-local-name="אסטונית" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Hilberten_espazio" title="Hilberten espazio – בסקית" lang="eu" hreflang="eu" data-title="Hilberten espazio" data-language-autonym="Euskara" data-language-local-name="בסקית" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7%DB%8C_%D9%87%DB%8C%D9%84%D8%A8%D8%B1%D8%AA" title="فضای هیلبرت – פרסית" lang="fa" hreflang="fa" data-title="فضای هیلبرت" data-language-autonym="فارسی" data-language-local-name="פרסית" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Hilbertin_avaruus" title="Hilbertin avaruus – פינית" lang="fi" hreflang="fi" data-title="Hilbertin avaruus" data-language-autonym="Suomi" data-language-local-name="פינית" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Espace_de_Hilbert" title="Espace de Hilbert – צרפתית" lang="fr" hreflang="fr" data-title="Espace de Hilbert" data-language-autonym="Français" data-language-local-name="צרפתית" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Espazo_de_Hilbert" title="Espazo de Hilbert – גליסית" lang="gl" hreflang="gl" data-title="Espazo de Hilbert" data-language-autonym="Galego" data-language-local-name="גליסית" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Hilbert-t%C3%A9r" title="Hilbert-tér – הונגרית" lang="hu" hreflang="hu" data-title="Hilbert-tér" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%AB%D5%AC%D5%A2%D5%A5%D6%80%D5%BF%D5%B5%D5%A1%D5%B6_%D5%BF%D5%A1%D6%80%D5%A1%D5%AE%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Հիլբերտյան տարածություն – ארמנית" lang="hy" hreflang="hy" data-title="Հիլբերտյան տարածություն" data-language-autonym="Հայերեն" data-language-local-name="ארמנית" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ruang_Hilbert" title="Ruang Hilbert – אינדונזית" lang="id" hreflang="id" data-title="Ruang Hilbert" data-language-autonym="Bahasa Indonesia" data-language-local-name="אינדונזית" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hilbert-r%C3%BAm" title="Hilbert-rúm – איסלנדית" lang="is" hreflang="is" data-title="Hilbert-rúm" data-language-autonym="Íslenska" data-language-local-name="איסלנדית" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spazio_di_Hilbert" title="Spazio di Hilbert – איטלקית" lang="it" hreflang="it" data-title="Spazio di Hilbert" data-language-autonym="Italiano" data-language-local-name="איטלקית" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%92%E3%83%AB%E3%83%99%E3%83%AB%E3%83%88%E7%A9%BA%E9%96%93" title="ヒルベルト空間 – יפנית" lang="ja" hreflang="ja" data-title="ヒルベルト空間" data-language-autonym="日本語" data-language-local-name="יפנית" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%9E%90%EB%B2%A0%EB%A5%B4%ED%8A%B8_%EA%B3%B5%EA%B0%84" title="힐베르트 공간 – קוריאנית" lang="ko" hreflang="ko" data-title="힐베르트 공간" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82_%D0%BC%D0%B5%D0%B9%D0%BA%D0%B8%D0%BD%D0%B4%D0%B8%D0%B3%D0%B8" title="Гильберт мейкиндиги – קירגיזית" lang="ky" hreflang="ky" data-title="Гильберт мейкиндиги" data-language-autonym="Кыргызча" data-language-local-name="קירגיזית" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Hilberto_erdv%C4%97" title="Hilberto erdvė – ליטאית" lang="lt" hreflang="lt" data-title="Hilberto erdvė" data-language-autonym="Lietuvių" data-language-local-name="ליטאית" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%B8%D0%B9%D0%BD_%D0%BE%D1%80%D0%BE%D0%BD_%D0%B7%D0%B0%D0%B9" title="Хилбертийн орон зай – מונגולית" lang="mn" hreflang="mn" data-title="Хилбертийн орон зай" data-language-autonym="Монгол" data-language-local-name="מונגולית" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ruang_Hilbert" title="Ruang Hilbert – מלאית" lang="ms" hreflang="ms" data-title="Ruang Hilbert" data-language-autonym="Bahasa Melayu" data-language-local-name="מלאית" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Hilbertruimte" title="Hilbertruimte – הולנדית" lang="nl" hreflang="nl" data-title="Hilbertruimte" data-language-autonym="Nederlands" data-language-local-name="הולנדית" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Hilbertrom" title="Hilbertrom – נורווגית חדשה" lang="nn" hreflang="nn" data-title="Hilbertrom" data-language-autonym="Norsk nynorsk" data-language-local-name="נורווגית חדשה" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Hilbert-rom" title="Hilbert-rom – נורווגית ספרותית" lang="nb" hreflang="nb" data-title="Hilbert-rom" data-language-autonym="Norsk bokmål" data-language-local-name="נורווגית ספרותית" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B9%E0%A8%BF%E0%A8%B2%E0%A8%AC%E0%A8%B0%E0%A8%9F_%E0%A8%B8%E0%A8%AA%E0%A9%87%E0%A8%B8" title="ਹਿਲਬਰਟ ਸਪੇਸ – פנג׳אבי" lang="pa" hreflang="pa" data-title="ਹਿਲਬਰਟ ਸਪੇਸ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="פנג׳אבי" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przestrze%C5%84_Hilberta" title="Przestrzeń Hilberta – פולנית" lang="pl" hreflang="pl" data-title="Przestrzeń Hilberta" data-language-autonym="Polski" data-language-local-name="פולנית" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DB%81%D9%84%D8%A8%D8%B1%D9%B9_%D8%B3%D9%BE%DB%8C%D8%B3" title="ہلبرٹ سپیس – פנג׳בית מערבית" lang="pnb" hreflang="pnb" data-title="ہلبرٹ سپیس" data-language-autonym="پنجابی" data-language-local-name="פנג׳בית מערבית" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Espa%C3%A7o_de_Hilbert" title="Espaço de Hilbert – פורטוגזית" lang="pt" hreflang="pt" data-title="Espaço de Hilbert" data-language-autonym="Português" data-language-local-name="פורטוגזית" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Spa%C8%9Biu_Hilbert" title="Spațiu Hilbert – רומנית" lang="ro" hreflang="ro" data-title="Spațiu Hilbert" data-language-autonym="Română" data-language-local-name="רומנית" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D0%B8%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2%D0%BE_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE" title="Гильбертово пространство – רוסית" lang="ru" hreflang="ru" data-title="Гильбертово пространство" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – סקוטית" lang="sco" hreflang="sco" data-title="Hilbert space" data-language-autonym="Scots" data-language-local-name="סקוטית" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Hilbertov_prostor" title="Hilbertov prostor – סרבו-קרואטית" lang="sh" hreflang="sh" data-title="Hilbertov prostor" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="סרבו-קרואטית" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Hilbert_space" title="Hilbert space – אנגלית פשוטה" lang="en-simple" hreflang="en-simple" data-title="Hilbert space" data-language-autonym="Simple English" data-language-local-name="אנגלית פשוטה" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Hilbertov_priestor" title="Hilbertov priestor – סלובקית" lang="sk" hreflang="sk" data-title="Hilbertov priestor" data-language-autonym="Slovenčina" data-language-local-name="סלובקית" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Hilbertov_prostor" title="Hilbertov prostor – סלובנית" lang="sl" hreflang="sl" data-title="Hilbertov prostor" data-language-autonym="Slovenščina" data-language-local-name="סלובנית" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Hap%C3%ABsira_e_Hilbertit" title="Hapësira e Hilbertit – אלבנית" lang="sq" hreflang="sq" data-title="Hapësira e Hilbertit" data-language-autonym="Shqip" data-language-local-name="אלבנית" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A5%D0%B8%D0%BB%D0%B1%D0%B5%D1%80%D1%82%D0%BE%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D0%BE%D1%80" title="Хилбертов простор – סרבית" lang="sr" hreflang="sr" data-title="Хилбертов простор" data-language-autonym="Српски / srpski" data-language-local-name="סרבית" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Hilbertrum" title="Hilbertrum – שוודית" lang="sv" hreflang="sv" data-title="Hilbertrum" data-language-autonym="Svenska" data-language-local-name="שוודית" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Espasyong_Hilbert" title="Espasyong Hilbert – טאגאלוג" lang="tl" hreflang="tl" data-title="Espasyong Hilbert" data-language-autonym="Tagalog" data-language-local-name="טאגאלוג" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Hilbert_uzay%C4%B1" title="Hilbert uzayı – טורקית" lang="tr" hreflang="tr" data-title="Hilbert uzayı" data-language-autonym="Türkçe" data-language-local-name="טורקית" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%96%D0%BB%D1%8C%D0%B1%D0%B5%D1%80%D1%82%D1%96%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80" title="Гільбертів простір – אוקראינית" lang="uk" hreflang="uk" data-title="Гільбертів простір" data-language-autonym="Українська" data-language-local-name="אוקראינית" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Gilbert_fazosi" title="Gilbert fazosi – אוזבקית" lang="uz" hreflang="uz" data-title="Gilbert fazosi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="אוזבקית" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%C3%B4ng_gian_Hilbert" title="Không gian Hilbert – וייטנאמית" lang="vi" hreflang="vi" data-title="Không gian Hilbert" data-language-autonym="Tiếng Việt" data-language-local-name="וייטנאמית" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E7%A9%BA%E9%97%B4" title="希尔伯特空间 – סינית וו" lang="wuu" hreflang="wuu" data-title="希尔伯特空间" data-language-autonym="吴语" data-language-local-name="סינית וו" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E7%A9%BA%E9%97%B4" title="希尔伯特空间 – סינית" lang="zh" hreflang="zh" data-title="希尔伯特空间" data-language-autonym="中文" data-language-local-name="סינית" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E5%B8%8C%E7%88%BE%E4%BC%AF%E7%89%B9%E7%A9%BA%E9%96%93" title="希爾伯特空間 – סינית קלאסית" lang="lzh" hreflang="lzh" data-title="希爾伯特空間" data-language-autonym="文言" data-language-local-name="סינית קלאסית" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%9B%82%E6%8B%94%E7%A9%BA%E9%96%93" title="囂拔空間 – קנטונזית" lang="yue" hreflang="yue" data-title="囂拔空間" data-language-autonym="粵語" data-language-local-name="קנטונזית" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q190056#sitelinks-wikipedia" title="עריכת קישורים בין־לשוניים" class="wbc-editpage">עריכת הקישורים</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="מרחבי שם"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="צפייה בדף התוכן [c]" accesskey="c"><span>ערך</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/%D7%A9%D7%99%D7%97%D7%94:%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" rel="discussion" title="שיחה על דף התוכן [t]" accesskey="t"><span>שיחה</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="שינוי הגוון השפה" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label 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href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit" title="עריכת הדף הזה [v]" accesskey="v"><span>עריכה</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=history"><span>גרסאות קודמות</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> כללי </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D_%D7%9C%D7%9B%D7%90%D7%9F/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="רשימה של כל דפי הוויקי שמקשרים לדף הזה [j]" accesskey="j"><span>דפים המקושרים לכאן</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A9%D7%99%D7%A0%D7%95%D7%99%D7%99%D7%9D_%D7%91%D7%93%D7%A4%D7%99%D7%9D_%D7%94%D7%9E%D7%A7%D7%95%D7%A9%D7%A8%D7%99%D7%9D/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" rel="nofollow" title="השינויים האחרונים בדפים המקושרים מהדף הזה [k]" accesskey="k"><span>שינויים בדפים המקושרים</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%93%D7%A4%D7%99%D7%9D_%D7%9E%D7%99%D7%95%D7%97%D7%93%D7%99%D7%9D" title="רשימה של כל הדפים המיוחדים [q]" accesskey="q"><span>דפים מיוחדים</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&oldid=39850545" title="קישור קבוע לגרסה הזאת של הדף הזה"><span>קישור קבוע</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=info" title="מידע נוסף על הדף הזה"><span>מידע על הדף</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A6%D7%99%D7%98%D7%95%D7%98_%D7%93%D7%A3_%D7%96%D7%94&page=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&id=39850545&wpFormIdentifier=titleform" title="מידע איך לצטט את הדף הזה"><span>ציטוט הדף הזה</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9E%D7%A7%D7%A6%D7%A8_%D7%9B%D7%AA%D7%95%D7%91%D7%95%D7%AA&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%259E%25D7%25A8%25D7%2597%25D7%2591_%25D7%2594%25D7%2599%25D7%259C%25D7%2591%25D7%25A8%25D7%2598"><span>קבלת כתובת מקוצרת</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:QrCode&url=https%3A%2F%2Fhe.wikipedia.org%2Fwiki%2F%25D7%259E%25D7%25A8%25D7%2597%25D7%2591_%25D7%2594%25D7%2599%25D7%259C%25D7%2591%25D7%25A8%25D7%2598"><span>הורדת קוד QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> הדפסה/יצוא </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%A1%D7%A4%D7%A8&bookcmd=book_creator&referer=%D7%9E%D7%A8%D7%97%D7%91+%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98"><span>יצירת ספר</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:DownloadAsPdf&page=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=show-download-screen"><span>הורדה כ־PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&printable=yes" title="גרסה להדפסה של הדף הזה [p]" accesskey="p"><span>גרסה להדפסה</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> במיזמים אחרים </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Hilbert_space" hreflang="en"><span>ויקישיתוף</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q190056" title="קישור לפריט המשויך במאגר הנתונים [g]" accesskey="g"><span>פריט ויקינתונים</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="כלי דף"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="מראה"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">מראה</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">הסתרה</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">מתוך ויקיפדיה, האנציקלופדיה החופשית</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-rtl mw-parser-output" lang="he" dir="rtl"><p><b>מרחב הילברט</b> הוא <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a> שהוא <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99_%D7%A9%D7%9C%D7%9D" title="מרחב מטרי שלם">מרחב מטרי שלם</a> ביחס ל<a href="/wiki/%D7%A0%D7%95%D7%A8%D7%9E%D7%94_(%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94)" title="נורמה (אנליזה)">נורמה</a> שמשרה המכפלה הפנימית שלו, בדרך כלל מממד אינסופי. מרחבי הילברט קרויים על שם ה<a href="/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%90%D7%99" title="מתמטיקאי">מתמטיקאי</a> הנודע <a href="/wiki/%D7%93%D7%95%D7%99%D7%93_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="דויד הילברט">דויד הילברט</a> ונודעת להם חשיבות רבה במסגרת תורת <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99%D7%AA" title="אנליזה פונקציונלית">האנליזה הפונקציונלית</a>. </p><p>מרחבי הילברט מאפשרים יישום של מושגים <a href="/wiki/%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="גאומטריה">גאומטריים</a> בסיסיים כגון <a href="/wiki/%D7%94%D7%98%D7%9C%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="הטלה (מתמטיקה)">הטלה</a> ו<a href="/wiki/%D7%91%D7%A1%D7%99%D7%A1_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="בסיס (אלגברה)">שינוי בסיס</a>, על מרחבים בעלי ממדים אינסופיים כדוגמת ה<a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99&action=edit&redlink=1" class="new" title="מרחב פונקציונלי (הדף אינו קיים)">מרחבים הפונקציונליים</a>. הם מספקים הקשר איתו ניתן לעצב ולהכליל את המושגים של <a href="/wiki/%D7%98%D7%95%D7%A8_%D7%A4%D7%95%D7%A8%D7%99%D7%99%D7%94" title="טור פורייה">טור פורייה</a> במונחים של <a href="/w/index.php?title=%D7%A4%D7%95%D7%9C%D7%99%D7%A0%D7%95%D7%9E%D7%99%D7%9D_%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%99%D7%9D&action=edit&redlink=1" class="new" title="פולינומים אורתוגונליים (הדף אינו קיים)">פולינומים אורתוגונליים</a> שרירותיים ושל <a href="/wiki/%D7%94%D7%AA%D7%9E%D7%A8%D7%AA_%D7%A4%D7%95%D7%A8%D7%99%D7%99%D7%94" title="התמרת פורייה">התמרת פורייה</a>. כמו כן, מרחבי הילברט הם בעלי חשיבות מכרעת בניסוח <a href="/wiki/%D7%9E%D7%9B%D7%A0%D7%99%D7%A7%D7%AA_%D7%94%D7%A7%D7%95%D7%95%D7%A0%D7%98%D7%99%D7%9D" title="מכניקת הקוונטים">מכניקת הקוונטים</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="הגדרה"><span id=".D7.94.D7.92.D7.93.D7.A8.D7.94"></span>הגדרה</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=1" title="עריכת קוד המקור של הפרק: הגדרה"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=1" title="עריכת פסקה: "הגדרה"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>מרחב הילברט</b> הוא <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a> (<a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב וקטורי</a> בעל <a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" class="mw-redirect" title="מכפלה פנימית">מכפלה פנימית</a>) שהוא <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99_%D7%A9%D7%9C%D7%9D" title="מרחב מטרי שלם">מרחב מטרי שלם</a> ביחס ל<a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A7%D7%94" title="מטריקה">מטריקה</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle d(x,y)={\sqrt {\langle x-y,x-y\rangle }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mo fence="false" stretchy="false">⟨</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo>,</mo> <mi>x</mi> <mo>−</mo> <mi>y</mi> <mo fence="false" stretchy="false">⟩</mo> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d(x,y)={\sqrt {\langle x-y,x-y\rangle }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b793babe4c7f86c7e2bd3aff7c798bfc0625e75f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:25.461ex; height:4.843ex;" alt="{\displaystyle d(x,y)={\sqrt {\langle x-y,x-y\rangle }}}"></span> שמשרה המכפלה הפנימית. </p><p>בפרט, מרחב הילברט חייב להיות מרחב וקטורי מעל ל<a href="/wiki/%D7%A9%D7%93%D7%94_(%D7%9E%D7%91%D7%A0%D7%94_%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%99)" title="שדה (מבנה אלגברי)">שדה</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99_%D7%A9%D7%9C%D7%9D" title="מרחב מטרי שלם">שלם</a> כמו <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים">שדה המספרים הממשיים</a> או <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%A8%D7%95%D7%9B%D7%91%D7%99%D7%9D" title="שדה המספרים המרוכבים">שדה המספרים המרוכבים</a>. לדוגמה, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span> הוא מרחב הילברט (ביחס לכל מכפלה פנימית), בעוד ש- <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce1121a4a9ff1c9f6b3e51008a1a1411b8f46231" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.027ex; height:2.676ex;" alt="{\displaystyle \mathbb {Q} ^{n}}"></span> איננו כזה. </p> <div class="mw-heading mw-heading2"><h2 id="המרחב_L2"><span id=".D7.94.D7.9E.D7.A8.D7.97.D7.91_L2"></span>המרחב <i>L<sup>2</sup></i></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=2" title="עריכת קוד המקור של הפרק: המרחב L2"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=2" title="עריכת פסקה: "המרחב L2"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>המרחב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584c65b4006a27b3155c51e6054fae6202764d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.426ex; height:3.176ex;" alt="{\displaystyle L^{2}(X)}"></span> כאשר <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X\subset \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> <mo>⊂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X\subset \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71afe1acdf6107bac3e40fa236a6ee59459006e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.757ex; height:2.176ex;" alt="{\displaystyle X\subset \mathbb {R} }"></span> הוא אחד מהמרחבים הפונקציונליים ומרחבי הילברט החשובים ביותר. </p><p>מרחב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584c65b4006a27b3155c51e6054fae6202764d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.426ex; height:3.176ex;" alt="{\displaystyle L^{2}(X)}"></span> מוגדר להיות כקבוצת כל ה"<a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94" title="פונקציה">פונקציות</a>" <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f:X\to \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:X\to \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a57fe120f564b03d50ef328f6a5e09d0e860781e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.488ex; height:2.509ex;" alt="{\displaystyle f:X\to \mathbb {C} }"></span> שהן <a href="/wiki/%D7%90%D7%99%D7%A0%D7%98%D7%92%D7%A8%D7%91%D7%99%D7%9C%D7%99%D7%95%D7%AA_%D7%9C%D7%91%D7%92" class="mw-redirect" title="אינטגרביליות לבג">אינטגרביליות לבג</a> בריבוע על הקבוצה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77c9459aca0b4981e1f3933b8354b37ea3049dc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.367ex; height:2.176ex;" alt="{\displaystyle \,X}"></span> (ראו הערה בהמשך). כלומר, האינטגרל לפי לבג קיים ומתקיים <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \int _{X}{|f|^{2}d\mu }=\int _{X}{|f(t)|^{2}dt}<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>μ</mi> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mi>d</mi> <mi>t</mi> </mrow> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \int _{X}{|f|^{2}d\mu }=\int _{X}{|f(t)|^{2}dt}<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6c0f40e388aaa867878e8e9d8bee38ab7637e56" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:29.72ex; height:5.676ex;" alt="{\displaystyle \int _{X}{|f|^{2}d\mu }=\int _{X}{|f(t)|^{2}dt}<\infty }"></span> (כאשר <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,\mu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>μ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,\mu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/745951ff5642eef22ccff7952a964ec0be349202" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.789ex; height:2.176ex;" alt="{\displaystyle \,\mu }"></span> היא <a href="/wiki/%D7%9E%D7%99%D7%93%D7%AA_%D7%9C%D7%91%D7%92" title="מידת לבג">מידת לבג</a>). אז מסמנים ש <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f\in L^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>∈</mo> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\in L^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0857c2506983134ce2848773f3b906f8ff97689d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.546ex; height:3.176ex;" alt="{\displaystyle f\in L^{2}(X)}"></span>. מרחב זה, עם פעולת חיבור פונקציות וכפל בסקלר הוא <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב וקטורי</a>. </p><p>יתרה מכך, הוא מרחב הילברט עם <a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" class="mw-redirect" title="מכפלה פנימית">המכפלה הפנימית</a> הבאה: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle f,g\rangle =\int _{X}{f(t)g^{*}(t)dt}=\int _{X}{f(t){\overline {g(t)}}dt}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>f</mi> <mo>,</mo> <mi>g</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>t</mi> </mrow> <mo>=</mo> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mi>d</mi> <mi>t</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle f,g\rangle =\int _{X}{f(t)g^{*}(t)dt}=\int _{X}{f(t){\overline {g(t)}}dt}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e4ea41994290f85ff6904e098c4f9395b572819" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:38.726ex; height:5.676ex;" alt="{\displaystyle \langle f,g\rangle =\int _{X}{f(t)g^{*}(t)dt}=\int _{X}{f(t){\overline {g(t)}}dt}}"></span></dd></dl> <p>כאשר * (או קו עליון) מסמנים <a href="/wiki/%D7%A6%D7%9E%D7%95%D7%93_%D7%9E%D7%A8%D7%95%D7%9B%D7%91" title="צמוד מרוכב">צמוד מרוכב</a>. </p><p>הערה לגבי איברי <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584c65b4006a27b3155c51e6054fae6202764d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.426ex; height:3.176ex;" alt="{\displaystyle L^{2}(X)}"></span>: לפי בניית <a href="/wiki/%D7%90%D7%99%D7%A0%D7%98%D7%92%D7%A8%D7%9C_%D7%9C%D7%91%D7%92" title="אינטגרל לבג">אינטגרל לבג</a>, עולה שאין שום דרך להבחין בין שתי פונקציות <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> ו-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> הנבדלות אחת מהשנייה רק על <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%9E%D7%9E%D7%99%D7%93%D7%94_%D7%90%D7%A4%D7%A1" title="קבוצה ממידה אפס">קבוצה ממידה אפס</a> באמצעות המכפלה הפנימית או הנורמה. לכן, הנורמה של כל פונקציה ששונה מאפס רק על קבוצה ממידה אפס היא <a href="/wiki/0_(%D7%9E%D7%A1%D7%A4%D7%A8)" title="0 (מספר)">אפס</a>. מצב זה עומד בניגוד לאקסיומות ה<a href="/wiki/%D7%A0%D7%95%D7%A8%D7%9E%D7%94_(%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94)" title="נורמה (אנליזה)">נורמה</a> שדורשות: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \|f\|=0\iff f=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mi>f</mi> <mo fence="false" stretchy="false">‖</mo> <mo>=</mo> <mn>0</mn> <mspace width="thickmathspace" /> <mo stretchy="false">⟺</mo> <mspace width="thickmathspace" /> <mi>f</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|f\|=0\iff f=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05dfc7ff092a36921abe136ac0d88f88b2277410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.301ex; height:2.843ex;" alt="{\displaystyle \|f\|=0\iff f=0}"></span>. כדי לתקן מצב זה, מרחב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/584c65b4006a27b3155c51e6054fae6202764d9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.426ex; height:3.176ex;" alt="{\displaystyle L^{2}(X)}"></span> אינו מוגדר על פונקציות אלא על <a href="/wiki/%D7%9E%D7%97%D7%9C%D7%A7%D7%AA_%D7%A9%D7%A7%D7%99%D7%9C%D7%95%D7%AA" title="מחלקת שקילות">מחלקות השקילות</a> שלהן, שנקבעות לפי <a href="/wiki/%D7%99%D7%97%D7%A1_%D7%A9%D7%A7%D7%99%D7%9C%D7%95%D7%AA" title="יחס שקילות">יחס השקילות</a> הבא: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=g\ \ {\mbox{a.e.}}\ \ \equiv f\sim g\iff \mu \left(\left\{x\in X|f(x)\neq g(x)\right\}\right)=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mi>g</mi> <mtext> </mtext> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>a.e.</mtext> </mstyle> </mrow> <mtext> </mtext> <mtext> </mtext> <mo>≡</mo> <mi>f</mi> <mo>∼</mo> <mi>g</mi> <mspace width="thickmathspace" /> <mo stretchy="false">⟺</mo> <mspace width="thickmathspace" /> <mi>μ</mi> <mrow> <mo>(</mo> <mrow> <mo>{</mo> <mrow> <mi>x</mi> <mo>∈</mo> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>≠</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>}</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=g\ \ {\mbox{a.e.}}\ \ \equiv f\sim g\iff \mu \left(\left\{x\in X|f(x)\neq g(x)\right\}\right)=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/417463f94472615d2fb46aa3dbf26e13cabb6864" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:55.545ex; height:2.843ex;" alt="{\displaystyle f=g\ \ {\mbox{a.e.}}\ \ \equiv f\sim g\iff \mu \left(\left\{x\in X|f(x)\neq g(x)\right\}\right)=0}"></span></dd></dl> <p>כלומר: כל שתי פונקציות <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> ו-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>g</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3556280e66fe2c0d0140df20935a6f057381d77" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.116ex; height:2.009ex;" alt="{\displaystyle g}"></span> הנבדלות אחת מהשנייה רק על קבוצה ממידה אפס הן שקולות ומחלקת השקילות שלהן היא איבר במרחב זה. ניתן להגדיר את כל הפעולות הליניאריות על המחלקות באמצעות ביצוע פעולות אלה על הנציגים של כל מחלקה. הגדרה זו טובה והמרחב שמתקבל הוא מוגדר היטב והוא מרחב הילברט. </p> <div class="mw-heading mw-heading2"><h2 id="דוגמאות_נוספות"><span id=".D7.93.D7.95.D7.92.D7.9E.D7.90.D7.95.D7.AA_.D7.A0.D7.95.D7.A1.D7.A4.D7.95.D7.AA"></span>דוגמאות נוספות</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=3" title="עריכת קוד המקור של הפרק: דוגמאות נוספות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=3" title="עריכת פסקה: "דוגמאות נוספות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>המרחב האוקלידי <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span> עם הנורמה האוקלידית הוא מרחב הילברט.</li> <li>המרחב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {C} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a53b4e76242764d1bca004168353c380fef25258" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {C} ^{n}}"></span> עם המכפלה הפנימית: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle z,w\rangle =\sum _{k=1}^{n}{{z_{k}}{\overline {w_{k}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>z</mi> <mo>,</mo> <mi>w</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>w</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle z,w\rangle =\sum _{k=1}^{n}{{z_{k}}{\overline {w_{k}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d8980e9a82b7e782f4c424b7f697efff91c3a558" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:17.474ex; height:6.843ex;" alt="{\displaystyle \langle z,w\rangle =\sum _{k=1}^{n}{{z_{k}}{\overline {w_{k}}}}}"></span> הוא מרחב הילברט.</li> <li>מרחב הסדרות האינסופיות: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ell _{2}=\left\{(x_{n})_{n=1,\dots }|x_{n}\in \mathbb {C} ,\sum _{n\in \mathbb {N} }\left|x_{n}\right|^{2}<\infty \right\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> <mo>,</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </munder> <msup> <mrow> <mo>|</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo><</mo> <mi mathvariant="normal">∞</mi> </mrow> <mo>}</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{2}=\left\{(x_{n})_{n=1,\dots }|x_{n}\in \mathbb {C} ,\sum _{n\in \mathbb {N} }\left|x_{n}\right|^{2}<\infty \right\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ea4fd53ce3222db50d3dd1fdb00bd06e6670e5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:41.736ex; height:7.509ex;" alt="{\displaystyle \ell _{2}=\left\{(x_{n})_{n=1,\dots }|x_{n}\in \mathbb {C} ,\sum _{n\in \mathbb {N} }\left|x_{n}\right|^{2}<\infty \right\}}"></span>, מצויד במכפלה הפנימית <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle x,y\rangle =\sum _{n\in \mathbb {N} }x_{n}{\overline {y_{n}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo fence="false" stretchy="false">⟩</mo> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle x,y\rangle =\sum _{n\in \mathbb {N} }x_{n}{\overline {y_{n}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3f7530c078a851f4b31200267c56a4da7165205b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.19ex; height:5.676ex;" alt="{\displaystyle \langle x,y\rangle =\sum _{n\in \mathbb {N} }x_{n}{\overline {y_{n}}}}"></span>, הוא מרחב הילברט.</li></ul> <div class="mw-heading mw-heading2"><h2 id="בניות"><span id=".D7.91.D7.A0.D7.99.D7.95.D7.AA"></span>בניות</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=4" title="עריכת קוד המקור של הפרק: בניות"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=4" title="עריכת פסקה: "בניות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="סכום_ישר_של_מרחבי_הילברט"><span id=".D7.A1.D7.9B.D7.95.D7.9D_.D7.99.D7.A9.D7.A8_.D7.A9.D7.9C_.D7.9E.D7.A8.D7.97.D7.91.D7.99_.D7.94.D7.99.D7.9C.D7.91.D7.A8.D7.98"></span>סכום ישר של מרחבי הילברט</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=5" title="עריכת קוד המקור של הפרק: סכום ישר של מרחבי הילברט"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=5" title="עריכת פסקה: "סכום ישר של מרחבי הילברט"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b3de4facc7bd3250b910c4363111ae952f7446f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.018ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{1}}"></span> ו-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a40a9c1d9df2f248ea15869968cef102c511684" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.018ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{2}}"></span> הם מרחבי הילברט, ניתן ליצור מהם מרחב וקטורי חדש הקרוי <a href="/wiki/%D7%A1%D7%9B%D7%95%D7%9D_%D7%99%D7%A9%D7%A8" title="סכום ישר">הסכום הישר</a> שלהם ומסומן <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⊕</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f45657e708ce46e4370bdc2bff9b3534f5715e28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.876ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}"></span>. כקבוצה, מרחב זה הוא <a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A7%D7%A8%D7%98%D7%96%D7%99%D7%AA" title="מכפלה קרטזית">המכפלה הקרטזית</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{1}\times {\mathcal {H}}_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>×</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{1}\times {\mathcal {H}}_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14ffc832d3a6dffa9dbe353e70d8006a475d9247" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.876ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{1}\times {\mathcal {H}}_{2}}"></span>. החיבור והכפל בסקלר מוגדרים נקודתית והמכפלה הפנימית מוגדרת באופן הבא: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle (x_{1},x_{2}),(y_{1},y_{2})\rangle _{{\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}=\langle x_{1},y_{1}\rangle _{{\mathcal {H}}_{1}}+\langle x_{2},y_{2}\rangle _{{\mathcal {H}}_{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mo stretchy="false">(</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⊕</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mo fence="false" stretchy="false">⟩</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle (x_{1},x_{2}),(y_{1},y_{2})\rangle _{{\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}=\langle x_{1},y_{1}\rangle _{{\mathcal {H}}_{1}}+\langle x_{2},y_{2}\rangle _{{\mathcal {H}}_{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84e5ee99ac288f532aa4f49c9f26b987d4b8b342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:49.321ex; height:3.009ex;" alt="{\displaystyle \langle (x_{1},x_{2}),(y_{1},y_{2})\rangle _{{\mathcal {H}}_{1}\oplus {\mathcal {H}}_{2}}=\langle x_{1},y_{1}\rangle _{{\mathcal {H}}_{1}}+\langle x_{2},y_{2}\rangle _{{\mathcal {H}}_{2}}}"></span>.</dd></dl> <p>כאמור, המרחב המתקבל הוא מרחב הילברט. באופן כללי, אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{{\mathcal {H}}_{i}\right\}_{i\in I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>{</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>}</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{{\mathcal {H}}_{i}\right\}_{i\in I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d8d3eb200b92700ff79d6b34fd2b3110bc7d436" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.813ex; height:3.009ex;" alt="{\displaystyle \left\{{\mathcal {H}}_{i}\right\}_{i\in I}}"></span> היא משפחה כלשהי של מרחבי הילברט, סכומם הישר מוגדר באופן הבא: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bigoplus _{i\in I}{\mathcal {H}}_{i}=\left\{\left(x_{i}\right)_{i\in I}:x_{i}\in {\mathcal {H}}_{i}\ \forall i,\ \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty \right\}\subseteq \prod _{i\in I}{\mathcal {H}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>⨁</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mrow> <mo>{</mo> <mrow> <msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </msub> <mo>:</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>∈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mtext> </mtext> <mi mathvariant="normal">∀</mi> <mi>i</mi> <mo>,</mo> <mtext> </mtext> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msup> <mrow> <mo symmetric="true">‖</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo symmetric="true">‖</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo><</mo> <mi mathvariant="normal">∞</mi> </mrow> <mo>}</mo> </mrow> <mo>⊆</mo> <munder> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bigoplus _{i\in I}{\mathcal {H}}_{i}=\left\{\left(x_{i}\right)_{i\in I}:x_{i}\in {\mathcal {H}}_{i}\ \forall i,\ \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty \right\}\subseteq \prod _{i\in I}{\mathcal {H}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1e2fe8c1591138aa7ddbfdff35f4672f8571e0e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:58.408ex; height:7.509ex;" alt="{\displaystyle \bigoplus _{i\in I}{\mathcal {H}}_{i}=\left\{\left(x_{i}\right)_{i\in I}:x_{i}\in {\mathcal {H}}_{i}\ \forall i,\ \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty \right\}\subseteq \prod _{i\in I}{\mathcal {H}}_{i}}"></span>.</dd></dl> <p>כאן הסכום <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msup> <mrow> <mo symmetric="true">‖</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo symmetric="true">‖</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0ac5bcb66bd0a8a69d0479a846e4a09d4768c71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:9.251ex; height:5.676ex;" alt="{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}}"></span> מפורש כסופרמום של <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{j\in J}\left\Vert x_{j}\right\Vert ^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>∈</mo> <mi>J</mi> </mrow> </munder> <msup> <mrow> <mo symmetric="true">‖</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo symmetric="true">‖</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{j\in J}\left\Vert x_{j}\right\Vert ^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33e635fe1ee019b8184da4cc61f72b5d9b222217" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:9.361ex; height:5.843ex;" alt="{\displaystyle \sum _{j\in J}\left\Vert x_{j}\right\Vert ^{2}}"></span> על פני כל תת-הקבוצות הסופיות <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle J\subseteq I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>J</mi> <mo>⊆</mo> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle J\subseteq I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76ac10d0192d1da551ee96115a645f1faa4465de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.742ex; height:2.343ex;" alt="{\displaystyle J\subseteq I}"></span>. התנאי <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msup> <mrow> <mo symmetric="true">‖</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo symmetric="true">‖</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c8ef52bfe433b6d62f1d33e1e8629a5aad14beca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:14.673ex; height:5.676ex;" alt="{\displaystyle \sum _{i\in I}\left\Vert x_{i}\right\Vert ^{2}<\infty }"></span> גורר בפרט ש-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/491e215fe273840aab63acab32e73cb14f2fc8e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.39ex; height:2.509ex;" alt="{\displaystyle x_{i}=0}"></span> לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> פרט למספר <a href="/wiki/%D7%91%D7%9F_%D7%9E%D7%A0%D7%99%D7%99%D7%94" class="mw-redirect" title="בן מנייה">בן מנייה</a> של אינדקסים ב-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span>. </p><p>כמו קודם, החיבור והכפל בסקלר מוגדרים נקודתית והמכפלה הפנימית מוגדרת לפי </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle x,y\right\rangle =\sum _{i\in I}\left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>y</mi> </mrow> <mo>⟩</mo> </mrow> <mo>=</mo> <munder> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msub> <mrow> <mo>⟨</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle x,y\right\rangle =\sum _{i\in I}\left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bc8e24d41ea08eaa37268ca29a0bec5b71c6cc4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:21.326ex; height:5.676ex;" alt="{\displaystyle \left\langle x,y\right\rangle =\sum _{i\in I}\left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}"></span></dd></dl> <p>כאשר <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>⟨</mo> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a1875240502befd2a65773cd58e40d43f27e3b27" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:9.157ex; height:3.176ex;" alt="{\displaystyle \left\langle x_{i},y_{i}\right\rangle _{{\mathcal {H}}_{i}}}"></span> היא המכפלה הפנימית על <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a46acfbe3a5800ed8ab10a1233caadd4304921ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.763ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{i}}"></span>. בכך מקבלים מרחב הילברט שכל אחד מהמרחבים <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a46acfbe3a5800ed8ab10a1233caadd4304921ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.763ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{i}}"></span> משוכן בו כ<a href="/wiki/%D7%AA%D7%AA-%D7%9E%D7%A8%D7%97%D7%91" class="mw-redirect" title="תת-מרחב">תת-מרחב</a> <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A1%D7%92%D7%95%D7%A8%D7%94" title="קבוצה סגורה">סגור</a>. בנוסף לכך, תתי-מרחבים אלה הם <a href="/wiki/%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%95%D7%AA" title="אורתוגונליות">אורתוגונליים</a> זה לזה. </p><p>קיים גם מושג של "סכום ישר פנימי". אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}"></span> הוא מרחב הילברט ונתונה משפחה של תתי-מרחבים <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{V_{i}\right\}_{i\in I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>}</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{V_{i}\right\}_{i\in I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e37d639d65c5736a87f4c00098fa41661826f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.204ex; height:3.009ex;" alt="{\displaystyle \left\{V_{i}\right\}_{i\in I}}"></span> סגורים ואורתוגונליים זה לזה כך ש-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{span}}\left(\bigcup _{i\in I}V_{i}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>span</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </munder> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{span}}\left(\bigcup _{i\in I}V_{i}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/29ef8759d1bd7e329149d93b14c933d43e244638" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.856ex; height:7.509ex;" alt="{\displaystyle {\mbox{span}}\left(\bigcup _{i\in I}V_{i}\right)}"></span> היא <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A6%D7%A4%D7%95%D7%A4%D7%94" title="קבוצה צפופה">קבוצה צפופה</a> ב-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}"></span>, אז אומרים ש-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}"></span> הוא סכום ישר פנימי של המרחבים <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\{V_{i}\right\}_{i\in I}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>{</mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>}</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>∈</mo> <mi>I</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\{V_{i}\right\}_{i\in I}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e37d639d65c5736a87f4c00098fa41661826f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.204ex; height:3.009ex;" alt="{\displaystyle \left\{V_{i}\right\}_{i\in I}}"></span> ובמקרה זה הוא <a href="/wiki/%D7%90%D7%99%D7%96%D7%95%D7%9E%D7%95%D7%A8%D7%A4%D7%99%D7%96%D7%9D" title="איזומורפיזם">איזומורפי</a> באופן קנוני לסכום הישר החיצוני שלהם. כל סכום ישר (חיצוני או פנימי) מצויד במשפחה של <a href="/w/index.php?title=%D7%94%D7%98%D7%9C%D7%94_%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%AA&action=edit&redlink=1" class="new" title="הטלה אורתוגונלית (הדף אינו קיים)">הטלות אורתוגונליות</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ba1396129f7be3c7f828a571b6649e6807d10d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.292ex; height:2.509ex;" alt="{\displaystyle P_{i}}"></span>, כאשר <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ba1396129f7be3c7f828a571b6649e6807d10d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.292ex; height:2.509ex;" alt="{\displaystyle P_{i}}"></span> היא ההטלה על המרחב ה-i-י בסכום, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a46acfbe3a5800ed8ab10a1233caadd4304921ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.763ex; height:2.509ex;" alt="{\displaystyle {\mathcal {H}}_{i}}"></span>. הטלות אלה הן <a href="/w/index.php?title=%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%97%D7%A1%D7%95%D7%9D&action=edit&redlink=1" class="new" title="אופרטור חסום (הדף אינו קיים)">אופרטורים חסומים</a>, <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%94%D7%A8%D7%9E%D7%99%D7%98%D7%99" title="אופרטור הרמיטי">הרמיטיים</a> ו<a href="/wiki/%D7%90%D7%99%D7%93%D7%9E%D7%A4%D7%95%D7%98%D7%A0%D7%98" title="אידמפוטנט">אידמפוטנטיים</a> והן מקיימות את יחס האורתוגונליות: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{i}P_{j}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{i}P_{j}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/953532e2e100b5a28dfdd1c40d9e8e535c808817" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:8.955ex; height:2.843ex;" alt="{\displaystyle P_{i}P_{j}=0}"></span> לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i\neq j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> <mo>≠</mo> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i\neq j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d95aeb406bb427ac96806bc00c30c91d31b858be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.859ex; height:2.676ex;" alt="{\displaystyle i\neq j}"></span>. </p> <div class="mw-heading mw-heading3"><h3 id="מנה_של_מרחבי_הילברט"><span id=".D7.9E.D7.A0.D7.94_.D7.A9.D7.9C_.D7.9E.D7.A8.D7.97.D7.91.D7.99_.D7.94.D7.99.D7.9C.D7.91.D7.A8.D7.98"></span>מנה של מרחבי הילברט</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=6" title="עריכת קוד המקור של הפרק: מנה של מרחבי הילברט"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=6" title="עריכת פסקה: "מנה של מרחבי הילברט"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>אם <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19ef4c7b923a5125ac91aa491838a95ee15b804f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.964ex; height:2.176ex;" alt="{\displaystyle {\mathcal {H}}}"></span> הוא מרחב הילברט ו-<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span> הוא תת-מרחב סגור שלו, <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%A0%D7%94_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="מרחב מנה (אלגברה ליניארית)">מרחב המנה</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}/M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}/M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/239fe126896ea0ebe4e993eae5a376b10942705d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.568ex; height:2.843ex;" alt="{\displaystyle {\mathcal {H}}/M}"></span> הוא מרחב הילברט עם המכפלה הפנימית <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\langle x+M,y+M\right\rangle =\left\langle P\left(x\right),P\left(y\right)\right\rangle _{\mathcal {H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>M</mi> <mo>,</mo> <mi>y</mi> <mo>+</mo> <mi>M</mi> </mrow> <mo>⟩</mo> </mrow> <mo>=</mo> <msub> <mrow> <mo>⟨</mo> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>P</mi> <mrow> <mo>(</mo> <mi>y</mi> <mo>)</mo> </mrow> </mrow> <mo>⟩</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle x+M,y+M\right\rangle =\left\langle P\left(x\right),P\left(y\right)\right\rangle _{\mathcal {H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8673a05ff21feeeae9d41a13cf9414596fee3527" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:34.212ex; height:3.009ex;" alt="{\displaystyle \left\langle x+M,y+M\right\rangle =\left\langle P\left(x\right),P\left(y\right)\right\rangle _{\mathcal {H}}}"></span>, כאשר <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> היא ההטלה האורתוגונלית על <a href="/w/index.php?title=%D7%9E%D7%A9%D7%9C%D7%99%D7%9D_%D7%A0%D7%99%D7%A6%D7%91&action=edit&redlink=1" class="new" title="משלים ניצב (הדף אינו קיים)">המשלים הניצב</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M^{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M^{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae5a1a7b3924e331eff4b60dac12c654a9ce21e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.01ex; height:2.676ex;" alt="{\displaystyle M^{\bot }}"></span>. באופן זה מתקבל מרחב הילברט אשר איזומורפי <a href="/wiki/%D7%90%D7%99%D7%96%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="איזומטריה">איזומטרית</a> למרחב <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M^{\bot }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>M</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">⊥</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M^{\bot }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae5a1a7b3924e331eff4b60dac12c654a9ce21e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.01ex; height:2.676ex;" alt="{\displaystyle M^{\bot }}"></span>. ה<a href="/wiki/%D7%A0%D7%95%D7%A8%D7%9E%D7%94_(%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94)" title="נורמה (אנליזה)">נורמה</a> המושרית מהמכפלה הפנימית על <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {H}}/M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">H</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {H}}/M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/239fe126896ea0ebe4e993eae5a376b10942705d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.568ex; height:2.843ex;" alt="{\displaystyle {\mathcal {H}}/M}"></span> היא </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left\Vert x+M\right\Vert =d\left(x,M\right)=\inf _{m\in M}\left\Vert x-m\right\Vert }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo symmetric="true">‖</mo> <mrow> <mi>x</mi> <mo>+</mo> <mi>M</mi> </mrow> <mo symmetric="true">‖</mo> </mrow> <mo>=</mo> <mi>d</mi> <mrow> <mo>(</mo> <mrow> <mi>x</mi> <mo>,</mo> <mi>M</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">inf</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>∈</mo> <mi>M</mi> </mrow> </munder> <mrow> <mo symmetric="true">‖</mo> <mrow> <mi>x</mi> <mo>−</mo> <mi>m</mi> </mrow> <mo symmetric="true">‖</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\Vert x+M\right\Vert =d\left(x,M\right)=\inf _{m\in M}\left\Vert x-m\right\Vert }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9748cad98d97c0c15b6f3e7871eb39ac12d5d402" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:36.541ex; height:4.009ex;" alt="{\displaystyle \left\Vert x+M\right\Vert =d\left(x,M\right)=\inf _{m\in M}\left\Vert x-m\right\Vert }"></span>.</dd></dl> <div class="mw-heading mw-heading2"><h2 id="ראו_גם"><span id=".D7.A8.D7.90.D7.95_.D7.92.D7.9D"></span>ראו גם</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=7" title="עריכת קוד המקור של הפרק: ראו גם"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=7" title="עריכת פסקה: "ראו גם"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="אלגברה ליניארית">אלגברה ליניארית</a></li> <li><a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99%D7%AA" title="אנליזה פונקציונלית">אנליזה פונקציונלית</a></li> <li><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A" title="מרחב בנך">מרחב בנך</a></li> <li><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%94%D7%A6%D7%92%D7%94_%D7%A9%D7%9C_%D7%A8%D7%99%D7%A1" title="משפט ההצגה של ריס">משפט ההצגה של ריס</a></li> <li><a href="/wiki/%D7%98%D7%95%D7%A8_%D7%A4%D7%95%D7%A8%D7%99%D7%99%D7%94" title="טור פורייה">טור פורייה</a></li> <li><a href="/wiki/%D7%94%D7%AA%D7%9E%D7%A8%D7%AA_%D7%A4%D7%95%D7%A8%D7%99%D7%99%D7%94" title="התמרת פורייה">התמרת פורייה</a></li> <li><a href="/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%A9%D7%98%D7%95%D7%A8%D7%9D-%D7%9C%D7%99%D7%95%D7%91%D7%99%D7%9C" title="תורת שטורם-ליוביל">תורת שטורם-ליוביל</a></li> <li><a href="/wiki/%D7%A1%D7%99%D7%9E%D7%95%D7%9F_%D7%93%D7%99%D7%A8%D7%90%D7%A7" title="סימון דיראק">סימון דיראק</a></li> <li><a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98%D7%99" title="שדה הילברטי">שדה הילברטי</a></li> <li><a href="/wiki/%D7%94%D7%AA%D7%9B%D7%A0%D7%A1%D7%95%D7%AA_%D7%97%D7%9C%D7%A9%D7%94_(%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98)" title="התכנסות חלשה (מרחב הילברט)">התכנסות חלשה</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="קישורים_חיצוניים"><span id=".D7.A7.D7.99.D7.A9.D7.95.D7.A8.D7.99.D7.9D_.D7.97.D7.99.D7.A6.D7.95.D7.A0.D7.99.D7.99.D7.9D"></span>קישורים חיצוניים</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&action=edit&section=8" title="עריכת קוד המקור של הפרק: קישורים חיצוניים"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98&veaction=edit&section=8" title="עריכת פסקה: "קישורים חיצוניים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="sisterwikilinkT"><span typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/" title="ויקישיתוף"><img alt="ויקישיתוף" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> מדיה וקבצים בנושא <b><a href="https://commons.wikimedia.org/wiki/Category:Hilbert_space" class="extiw" title="commons:Category:Hilbert space">מרחב הילברט</a></b> ב<a href="/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A9%D7%99%D7%AA%D7%95%D7%A3" title="ויקישיתוף">וויקישיתוף</a></div> <ul><li><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/Hilbert-space">מרחב הילברט</a>, באתר <a href="/wiki/%D7%90%D7%A0%D7%A6%D7%99%D7%A7%D7%9C%D7%95%D7%A4%D7%93%D7%99%D7%94_%D7%91%D7%A8%D7%99%D7%98%D7%A0%D7%99%D7%A7%D7%94" title="אנציקלופדיה בריטניקה">אנציקלופדיה בריטניקה</a> <span dir="rtl" class="languageicon">(באנגלית)</span><style data-mw-deduplicate="TemplateStyles:r36549940">.mw-parser-output .languageicon{font-size:0.95em;font-weight:bold;color:#555}</style></li> <li><a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/HilbertSpace.html">מרחב הילברט</a>, באתר <a href="/wiki/MathWorld" title="MathWorld">MathWorld</a> <span dir="rtl" class="languageicon">(באנגלית)</span><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36549940"></li> <li><span typeof="mw:File"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5:National_Library_IL_logo.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/20px-National_Library_IL_logo.svg.png" decoding="async" width="20" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/30px-National_Library_IL_logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/df/National_Library_IL_logo.svg/40px-National_Library_IL_logo.svg.png 2x" data-file-width="512" data-file-height="397" /></a></span> <a rel="nofollow" class="external text" href="https://www.nli.org.il/he/a-topic/987007560453005171">מרחבי הילברט</a>, דף שער ב<a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="הספרייה הלאומית">ספרייה הלאומית</a></li></ul> <p><br /> </p> <table class="navbox nowraplinks mw-collapsible autocollapse" style="width: 90%; clear: both; margin: 0.5em auto; margin-top: 0.5em; margin-bottom: 0.5em; padding: 0.2em; text-align: right;"> <tbody><tr> <th colspan="3" style="text-align: center; padding-top: 0.1em; padding-bottom: 0.1em; color: black; background:#d1eeee; font-weight: bold;">נושאים ב<a href="/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="אלגברה ליניארית">אלגברה ליניארית</a> </th></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">מושגי יסוד </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%A9%D7%93%D7%94_(%D7%9E%D7%91%D7%A0%D7%94_%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%99)" title="שדה (מבנה אלגברי)">שדה</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב וקטורי</a> • <a href="/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="משוואה ליניארית">משוואה ליניארית</a> • <a href="/wiki/%D7%9E%D7%A2%D7%A8%D7%9B%D7%AA_%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%95%D7%AA_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%95%D7%AA" title="מערכת משוואות ליניאריות">מערכת משוואות ליניאריות</a> • <a href="/wiki/%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="העתקה ליניארית">העתקה ליניארית</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94" title="מטריצה">מטריצה</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%95%D7%A7%D7%98%D7%95%D7%A8_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" class="mw-redirect" title="וקטור (אלגברה)">וקטורים</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%A1%D7%A7%D7%9C%D7%A8_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="סקלר (מתמטיקה)">סקלר</a> • <a href="/wiki/%D7%9B%D7%A4%D7%9C_%D7%91%D7%A1%D7%A7%D7%9C%D7%A8" title="כפל בסקלר">כפל בסקלר</a> • <a href="/wiki/%D7%A6%D7%99%D7%A8%D7%95%D7%A3_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99" title="צירוף ליניארי">צירוף ליניארי</a> • <a href="/wiki/%D7%AA%D7%9C%D7%95%D7%AA_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="תלות ליניארית">תלות ליניארית</a> • <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A4%D7%95%D7%A8%D7%A9%D7%AA" title="קבוצה פורשת">קבוצה פורשת</a> • <a href="/wiki/%D7%91%D7%A1%D7%99%D7%A1_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="בסיס (אלגברה)">בסיס</a> • <a href="/wiki/%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="קואורדינטות (אלגברה)">וקטור קואורדינטות</a> • <a href="/wiki/%D7%9E%D7%9E%D7%93_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="ממד (אלגברה ליניארית)">ממד</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94" title="מטריצה">מטריצות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9B%D7%A4%D7%9C_%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%95%D7%AA" title="כפל מטריצות">כפל מטריצות</a> • <a href="/wiki/%D7%A9%D7%97%D7%9C%D7%95%D7%A3_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="שחלוף (מתמטיקה)">שחלוף</a> • <a href="/wiki/%D7%93%D7%98%D7%A8%D7%9E%D7%99%D7%A0%D7%A0%D7%98%D7%94" title="דטרמיננטה">דטרמיננטה</a> • <a href="/wiki/%D7%93%D7%99%D7%A8%D7%95%D7%92_%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%95%D7%AA" title="דירוג מטריצות">דירוג מטריצות</a> • <a href="/wiki/%D7%93%D7%A8%D7%92%D7%94_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="דרגה (אלגברה ליניארית)">דרגה</a> • <a href="/wiki/%D7%A2%D7%A7%D7%91%D7%94_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="עקבה (אלגברה)">עקבה</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%9E%D7%A6%D7%95%D7%A8%D7%A4%D7%AA" title="מטריצה מצורפת">מטריצה מצורפת</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%AA_%D7%9E%D7%A2%D7%91%D7%A8" title="מטריצת מעבר">מטריצת מעבר</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%9E%D7%A9%D7%95%D7%9C%D7%A9%D7%99%D7%AA" title="מטריצה משולשית">מטריצה משולשית</a> • <a href="/wiki/%D7%93%D7%9E%D7%99%D7%95%D7%9F_%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%95%D7%AA" title="דמיון מטריצות">דמיון מטריצות</a> • <a href="/wiki/%D7%A2%D7%A8%D7%9A_%D7%A2%D7%A6%D7%9E%D7%99" title="ערך עצמי">ערך עצמי</a> • <a href="/wiki/%D7%A4%D7%95%D7%9C%D7%99%D7%A0%D7%95%D7%9D_%D7%90%D7%95%D7%A4%D7%99%D7%99%D7%A0%D7%99" title="פולינום אופייני">פולינום אופייני</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%9C%D7%9B%D7%A1%D7%99%D7%A0%D7%94" title="מטריצה לכסינה">לכסון מטריצות</a> • <a href="/wiki/%D7%A6%D7%95%D7%A8%D7%AA_%D7%96%27%D7%95%D7%A8%D7%93%D7%9F" title="צורת ז'ורדן">צורת ז'ורדן</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="העתקה ליניארית">העתקות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="העתקה ליניארית">העתקה ליניארית</a> • <a href="/wiki/%D7%A7%D7%95%D7%90%D7%95%D7%A8%D7%93%D7%99%D7%A0%D7%98%D7%95%D7%AA_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="קואורדינטות (אלגברה)">קואורדינטות</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%9E%D7%99%D7%99%D7%A6%D7%92%D7%AA" class="mw-redirect" title="מטריצה מייצגת">מטריצה מייצגת</a> • <a href="/wiki/%D7%92%D7%A8%D7%A2%D7%99%D7%9F_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="גרעין (אלגברה)">גרעין</a> • <a href="/wiki/%D7%90%D7%A0%D7%93%D7%95%D7%9E%D7%95%D7%A8%D7%A4%D7%99%D7%96%D7%9D" title="אנדומורפיזם">אנדומורפיזם</a> • <a href="/wiki/%D7%90%D7%99%D7%96%D7%95%D7%9E%D7%95%D7%A8%D7%A4%D7%99%D7%96%D7%9D" title="איזומורפיזם">איזומורפיזם</a> • <a href="/wiki/%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%90%D7%A4%D7%99%D7%A0%D7%99%D7%AA" title="העתקה אפינית">העתקה אפינית</a> • <a href="/wiki/%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%A4%D7%A8%D7%95%D7%99%D7%A7%D7%98%D7%99%D7%91%D7%99%D7%AA" title="העתקה פרויקטיבית">העתקה פרויקטיבית</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחבי מכפלה פנימית</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A1%D7%A7%D7%9C%D7%A8%D7%99%D7%AA" title="מכפלה סקלרית">מכפלה סקלרית</a> • <a href="/wiki/%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="מכפלה וקטורית">מכפלה וקטורית</a> • <a href="/wiki/%D7%90%D7%95%D7%A8%D7%AA%D7%95%D7%92%D7%95%D7%A0%D7%9C%D7%99%D7%95%D7%AA" title="אורתוגונליות">אורתוגונליות</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%94_%D7%A1%D7%99%D7%9E%D7%98%D7%A8%D7%99%D7%AA" title="מטריצה סימטרית">מטריצה סימטרית</a> • <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%94%D7%A8%D7%9E%D7%99%D7%98%D7%99" title="אופרטור הרמיטי">אופרטור הרמיטי</a> • <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%90%D7%95%D7%A0%D7%99%D7%98%D7%A8%D7%99" title="אופרטור אוניטרי">אופרטור אוניטרי</a> • <a href="/wiki/%D7%98%D7%A8%D7%A0%D7%A1%D7%A4%D7%95%D7%A8%D7%9E%D7%A6%D7%99%D7%94_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99%D7%AA" class="mw-redirect" title="טרנספורמציה נורמלית">טרנספורמציה נורמלית</a> • <a href="/wiki/%D7%A0%D7%95%D7%A8%D7%9E%D7%94_(%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94)" title="נורמה (אנליזה)">נורמה</a> • <a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A7%D7%94" title="מטריקה">מטריקה</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="תבנית (אלגברה ליניארית)">תבניות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%91%D7%99%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA" title="תבנית ביליניארית">תבנית ביליניארית</a> • <a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%A1%D7%99%D7%9E%D7%98%D7%A8%D7%99%D7%AA" class="mw-redirect" title="תבנית סימטרית">תבנית סימטרית</a> • <a href="/w/index.php?title=%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%94%D7%A8%D7%9E%D7%99%D7%98%D7%99%D7%AA&action=edit&redlink=1" class="new" title="תבנית הרמיטית (הדף אינו קיים)">תבנית הרמיטית</a> • <a href="/w/index.php?title=%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%A1%D7%99%D7%9E%D7%A4%D7%9C%D7%A7%D7%98%D7%99%D7%AA_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)&action=edit&redlink=1" class="new" title="תבנית סימפלקטית (אלגברה ליניארית) (הדף אינו קיים)">תבנית סימפלקטית</a> • <a href="/wiki/%D7%97%D7%A4%D7%99%D7%A4%D7%AA_%D7%9E%D7%98%D7%A8%D7%99%D7%A6%D7%95%D7%AA" title="חפיפת מטריצות">חפיפת מטריצות</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%94%D7%AA%D7%9E%D7%93%D7%94_%D7%A9%D7%9C_%D7%A1%D7%99%D7%9C%D7%91%D7%A1%D7%98%D7%A8" title="משפט ההתמדה של סילבסטר">משפט סילבסטר</a> • <a href="/w/index.php?title=%D7%AA%D7%91%D7%A0%D7%99%D7%AA_%D7%9E%D7%95%D7%9C%D7%98%D7%99-%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA_%D7%90%D7%A0%D7%98%D7%99-%D7%A1%D7%99%D7%9E%D7%98%D7%A8%D7%99%D7%AA&action=edit&redlink=1" class="new" title="תבנית מולטי-ליניארית אנטי-סימטרית (הדף אינו קיים)">תבנית מולטי-ליניארית אנטי-סימטרית</a> • <a href="/wiki/%D7%90%D7%95%D7%A8%D7%99%D7%99%D7%A0%D7%98%D7%A6%D7%99%D7%94_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="אוריינטציה (אלגברה ליניארית)">אוריינטציה</a> • <a href="/w/index.php?title=%D7%A6%D7%A4%D7%99%D7%A4%D7%95%D7%AA_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D6%BC%D7%90%D7%A8%D7%99%D7%AA)&action=edit&redlink=1" class="new" title="צפיפות (אלגברה ליניּארית) (הדף אינו קיים)">צפיפות</a> • <a href="/wiki/%D7%98%D7%A0%D7%96%D7%95%D7%A8" title="טנזור">טנזור</a> </td></tr> </tbody></table> <div class="mobileonly"> <div class="mw-heading mw-heading3"><h3 id="עץ_מיון_של_מרחבים_וקטוריים_טופולוגיים"><span id=".D7.A2.D7.A5_.D7.9E.D7.99.D7.95.D7.9F_.D7.A9.D7.9C_.D7.9E.D7.A8.D7.97.D7.91.D7.99.D7.9D_.D7.95.D7.A7.D7.98.D7.95.D7.A8.D7.99.D7.99.D7.9D_.D7.98.D7.95.D7.A4.D7.95.D7.9C.D7.95.D7.92.D7.99.D7.99.D7.9D"></span><a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA:%D7%A2%D7%A5_%D7%9E%D7%99%D7%95%D7%9F_%D7%A9%D7%9C_%D7%9E%D7%A8%D7%97%D7%91%D7%99%D7%9D_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%99%D7%9D_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%99%D7%9D" title="תבנית:עץ מיון של מרחבים וקטוריים טופולוגיים">עץ מיון של מרחבים וקטוריים טופולוגיים</a></h3></div> <style data-mw-deduplicate="TemplateStyles:r40000942">.mw-parser-output table.DiagramTable{border-collapse:collapse;table-layout:auto;height:100%}.mw-parser-output .DiagramTable td{position:relative;padding:0px;text-align:center;vertical-align:middle;height:100%}.mw-parser-output .DiagramTable tr{}.mw-parser-output div.Diagram1{position:absolute;width:100%;height:100%;box-sizing:border-box;z-index:3;top:0}.mw-parser-output div.Diagram2{position:absolute;padding:2px;top:50%;left:50%;transform:translate(-50%,-50%)}.mw-parser-output div.Diagram3{position:absolute;top:0;right:0;height:1.8em}.mw-parser-output div.interval2{position:absolute;bottom:0;right:0;width:50%}.mw-parser-output div.interval4{position:absolute;bottom:0;left:0;height:50%}.mw-parser-output div.interval6{position:absolute;bottom:0;right:0;height:50%}.mw-parser-output div.interval8{position:absolute;top:0;right:0;width:50%}.mw-parser-output div.interval28{position:absolute;bottom:0;right:0;width:50%;height:100%}.mw-parser-output div.interval46{position:absolute;bottom:0;left:0;right:0;height:50%}.mw-parser-output .DiagramLegend td{text-align:right;padding:2px;vertical-align:text-top}</style> <table class="DiagramTable"> <tbody><tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב וקטורי טופולוגי">מרחב וקטורי טופולוגי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב וקטורי טופולוגי">מרחב וקטורי טופולוגי</a></div> <div class="Diagram3"></div> </div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="6" rowspan="5"><div style="position: relative; vertical-align:top; text-align: right; justify-content: center; align-items: center; padding: 5px; border: 2px solid black; border-radius: 5px; background-color: white; right:20px; width:calc(100% - 50px)"><b>מקרא:</b> <table class="DiagramLegend"> <tbody><tr> <td><span style="display:inline-block; border:2px solid black; vertical-align:text-top; border-radius:5px ;" title="#FFFFBE"><span style="display:block; padding:0; width:calc(1em * 1); height:1em ; background: #FFFFBE; border-radius:calc(5px - 2px );"> </span></span> </td> <td>מחלקה של מרחבים וקטוריים טופולוגיים (מעל <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span></a>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span style="display:inline-block; border:2px solid #78A6A6; vertical-align:text-top; border-radius:5px ;" title="#BEFFFF"><span style="display:block; padding:0; width:calc(1em * 1); height:1em ; background: #BEFFFF; border-radius:calc(5px - 2px );"> </span></span> </td> <td>דוגמה או קבוצת דוגמאות למרחבים וקטוריים טופולוגיים.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span style="display:inline-block; border-top:2px solid black; vertical-align:middle;"><span style="display:block; padding:0; width:1em ; height:0;"> </span></span> </td> <td>מסלול שיורד למטה מצביע על כך שהמחלקה התחתונה היא חלק מהמחלקה העליונה. </td></tr> <tr> <td><span style="display:inline-block; border-top:2px solid #78A6A6; vertical-align:middle;"><span style="display:block; padding:0; width:1em ; height:0;"> </span></span> </td> <td>חלק במסלול שרלוונטי רק לדוגמאות. </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \cap }"></span> </td> <td><span id="חיתוך" class="citation">מחלקה המהווה <a href="/wiki/%D7%97%D7%99%D7%AA%D7%95%D7%9A_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חיתוך (מתמטיקה)">חיתוך</a> של המחלקות שמכילות אותה ומופיעות בתרשים.</span> </td></tr></tbody></table></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%90%D7%95%D7%A1%D7%93%D7%95%D7%A8%D7%A3" title="מרחב האוסדורף">האוסדורף</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%90%D7%95%D7%A1%D7%93%D7%95%D7%A8%D7%A3" title="מרחב האוסדורף">האוסדורף</a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99%D7%96%D7%91%D7%99%D7%9C%D7%99" title="מרחב מטריזבילי">מטריזבילי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99%D7%96%D7%91%D7%99%D7%9C%D7%99" title="מרחב מטריזבילי">מטריזבילי</a></div> <div class="Diagram3"></div> </div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A9%D7%9C%D7%9D" class="mw-redirect" title="מרחב שלם">שלם</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A9%D7%9C%D7%9D" class="mw-redirect" title="מרחב שלם">שלם</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A7%D7%9E%D7%95%D7%A8_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA" title="מרחב קמור מקומית">מרחב קמור מקומית</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A7%D7%9E%D7%95%D7%A8_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA" title="מרחב קמור מקומית">מרחב קמור מקומית</a></div> <div class="Diagram3"></div> </div></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 4px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 4px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 4px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - -2px ); height:50%; border-top: 2px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 0px); border-left: 0px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid black; border-bottom: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - -2px ); height:50%; border-top: 0px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91-F&action=edit&redlink=1" class="new" title="מרחב-F (הדף אינו קיים)">מרחב-F</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91-F&action=edit&redlink=1" class="new" title="מרחב-F (הדף אינו קיים)">מרחב-F</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td>                              </td></tr> <tr><td></td><td></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr> <tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A8%D7%A0%D7%94_%D7%9E%D7%95%D7%A8%D7%99%D7%A1_%D7%A4%D7%A8%D7%A9%D7%94" title="רנה מוריס פרשה"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/75px-Frechet.jpeg" decoding="async" width="75" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/113px-Frechet.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/150px-Frechet.jpeg 2x" data-file-width="268" data-file-height="326" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב פרשה (הדף אינו קיים)">מרחב פרשה</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A8%D7%A0%D7%94_%D7%9E%D7%95%D7%A8%D7%99%D7%A1_%D7%A4%D7%A8%D7%A9%D7%94" title="רנה מוריס פרשה"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/75px-Frechet.jpeg" decoding="async" width="75" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/113px-Frechet.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/150px-Frechet.jpeg 2x" data-file-width="268" data-file-height="326" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב פרשה (הדף אינו קיים)">מרחב פרשה</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%93%D7%95%D7%90%D7%9C%D7%99_%D7%9C%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב דואלי לפרשה (הדף אינו קיים)">מרחב דואלי לפרשה</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%93%D7%95%D7%90%D7%9C%D7%99_%D7%9C%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב דואלי לפרשה (הדף אינו קיים)">מרחב דואלי לפרשה</a></div> <div class="Diagram3"></div> </div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%90%D7%9C%D7%9B%D7%A1%D7%A0%D7%93%D7%A8_%D7%92%D7%A8%D7%95%D7%98%D7%A0%D7%93%D7%99%D7%A7" title="אלכסנדר גרוטנדיק"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/75px-Alexander_Grothendieck_-_face.jpg" decoding="async" width="75" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/113px-Alexander_Grothendieck_-_face.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/150px-Alexander_Grothendieck_-_face.jpg 2x" data-file-width="156" data-file-height="198" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%92%D7%A8%D7%A2%D7%99%D7%A0%D7%99&action=edit&redlink=1" class="new" title="מרחב גרעיני (הדף אינו קיים)">מרחב גרעיני</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%90%D7%9C%D7%9B%D7%A1%D7%A0%D7%93%D7%A8_%D7%92%D7%A8%D7%95%D7%98%D7%A0%D7%93%D7%99%D7%A7" title="אלכסנדר גרוטנדיק"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/75px-Alexander_Grothendieck_-_face.jpg" decoding="async" width="75" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/113px-Alexander_Grothendieck_-_face.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/150px-Alexander_Grothendieck_-_face.jpg 2x" data-file-width="156" data-file-height="198" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%92%D7%A8%D7%A2%D7%99%D7%A0%D7%99&action=edit&redlink=1" class="new" title="מרחב גרעיני (הדף אינו קיים)">מרחב גרעיני</a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c913ced284ad05bd42c8f004a3a83dee6323cb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c913ced284ad05bd42c8f004a3a83dee6323cb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%99" title="מרחב נורמי">מרחב נורמי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%99" title="מרחב נורמי">מרחב נורמי</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 0px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:1;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A1%D7%98%D7%A4%D7%9F_%D7%91%D7%A0%D7%9A" title="סטפן בנך"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/75px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg" decoding="async" width="75" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/113px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/150px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 2x" data-file-width="348" data-file-height="467" /></a><figcaption></figcaption></figure><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A" title="מרחב בנך">מרחב בנך</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A1%D7%98%D7%A4%D7%9F_%D7%91%D7%A0%D7%9A" title="סטפן בנך"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/75px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg" decoding="async" width="75" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/113px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/150px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 2x" data-file-width="348" data-file-height="467" /></a><figcaption></figcaption></figure><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A" title="מרחב בנך">מרחב בנך</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dfc074a50ce00ca95d3dc94ebae8432e2949a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.337ex; height:3.176ex;" alt="{\displaystyle C^{-\infty }(S^{1})}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dfc074a50ce00ca95d3dc94ebae8432e2949a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.337ex; height:3.176ex;" alt="{\displaystyle C^{-\infty }(S^{1})}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94-Lp_%D7%91%D7%90%D7%95%D7%A4%D7%9F_%D7%9E%D7%A7%D7%95%D7%9E%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות ה-Lp באופן מקומי (הדף אינו קיים)"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{loc}^{p}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3b8f175d94399b4ef7a4ea13f6206fc06227d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.302ex; height:3.176ex;" alt="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94-Lp_%D7%91%D7%90%D7%95%D7%A4%D7%9F_%D7%9E%D7%A7%D7%95%D7%9E%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות ה-Lp באופן מקומי (הדף אינו קיים)"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{loc}^{p}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3b8f175d94399b4ef7a4ea13f6206fc06227d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.302ex; height:3.176ex;" alt="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c83d1af403f8fe4ad3b88bf35451369497d8c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.254ex; height:2.843ex;" alt="{\displaystyle C(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c83d1af403f8fe4ad3b88bf35451369497d8c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.254ex; height:2.843ex;" alt="{\displaystyle C(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr><tr><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA_%D7%91%D7%A2%D7%9C%D7%95%D7%AA_%D7%AA%D7%95%D7%9E%D7%9A_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות בעלות תומך קומפקטי (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{c}^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbf3b0bd3006d257867fee68628fcdd300e2f04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA_%D7%91%D7%A2%D7%9C%D7%95%D7%AA_%D7%AA%D7%95%D7%9E%D7%9A_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות בעלות תומך קומפקטי (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{c}^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbf3b0bd3006d257867fee68628fcdd300e2f04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"></td></tr><tr><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + -2px + 0px); height:50%; border-top: 0px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -2px - 1 * 2px); border-left: 2px solid black; z-index:1;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - -4px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr> <tr><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%93%D7%95%D7%93_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="דוד הילברט"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/75px-Hilbert.jpg" decoding="async" width="75" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/113px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/150px-Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption></figcaption></figure><a class="mw-selflink selflink">מרחב הילברט</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%93%D7%95%D7%93_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="דוד הילברט"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/75px-Hilbert.jpg" decoding="async" width="75" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/113px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/150px-Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption></figcaption></figure><a class="mw-selflink selflink">מרחב הילברט</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9463391c47586860b3c88f37dc709ebbcefd5a20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.439ex; height:3.009ex;" alt="{\displaystyle C^{-\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9463391c47586860b3c88f37dc709ebbcefd5a20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.439ex; height:3.009ex;" alt="{\displaystyle C^{-\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr><tr><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L1" class="mw-redirect" title="מרחב L1"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{1}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{1}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a86223fba658a5daf612b39d3e25495d548bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{1}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L1" class="mw-redirect" title="מרחב L1"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{1}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{1}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a86223fba658a5daf612b39d3e25495d548bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{1}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aecdea502af56c65e0d42c2e477eba765beefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.152ex; height:3.176ex;" alt="{\displaystyle C(S^{1})}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aecdea502af56c65e0d42c2e477eba765beefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.152ex; height:3.176ex;" alt="{\displaystyle C(S^{1})}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 0px solid black; border-top: 0px solid black;"></div> <div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div> <div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div> <div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 0px solid black; border-bottom: 0px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_Lp" title="מרחב Lp"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{p}(\mathbb {R} );p>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> <mo>;</mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{p}(\mathbb {R} );p>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e5b46d45a471a76e8e5c35bde8a6775cec087d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.594ex; height:2.843ex;" alt="{\displaystyle L^{p}(\mathbb {R} );p>1}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_Lp" title="מרחב Lp"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{p}(\mathbb {R} );p>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> <mo>;</mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{p}(\mathbb {R} );p>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e5b46d45a471a76e8e5c35bde8a6775cec087d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.594ex; height:2.843ex;" alt="{\displaystyle L^{p}(\mathbb {R} );p>1}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td></td><td></td> <td></td> <td></td> <td></td> <td></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 3px - 1 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 3px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 3px - 1 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 3px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid black; border-bottom: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr> <tr><td></td><td></td><td></td><td></td><td></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> (<a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים">ממשי</a>) <a href="/wiki/%D7%9E%D7%9E%D7%93_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="ממד (אלגברה ליניארית)">ממד</a> סופי - <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> (<a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים">ממשי</a>) <a href="/wiki/%D7%9E%D7%9E%D7%93_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="ממד (אלגברה ליניארית)">ממד</a> סופי - <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span></a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L2" class="mw-redirect" title="מרחב L2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8722fb232f689925a4baa0e4ba478e43ee346672" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{2}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L2" class="mw-redirect" title="מרחב L2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8722fb232f689925a4baa0e4ba478e43ee346672" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{2}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td></td> <td></td><td></td><td></td></tr> </tbody></table><div class="reflist references-small"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">^</a></span> <span class="reference-text">שמות התואר "וקטורי", "טופולוגי" ו"ממשי" מושמטים בדרך כלל משם המחלקה.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">^</a></span> <span class="reference-text">במרחבי הפונקציות בדוגמאות, ניתן להחליף את <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span></a> ב<a href="/wiki/%D7%99%D7%A8%D7%99%D7%A2%D7%94_%D7%97%D7%9C%D7%A7%D7%94" title="יריעה חלקה">יריעה חלקה</a> כלשהי ואת מעגל היחידה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60796c8d0c03cf575637d3202463b214d9635880" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.576ex; height:2.676ex;" alt="{\displaystyle S^{1}}"></span> ביריעה חלקה <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%AA" title="קבוצה קומפקטית">קומפקטית</a> כלשהי.</span> </li> </ol></div></div> </div> <div class="desktoponly"> <table class="mw-collapsible autocollapse navbox" style="width: 90%; margin: 0.5em auto;" cellspacing="3"> <tbody><tr> <th style="background-color:#b0c4de; background:#d1eeee; padding-top: 0.1em; padding-bottom: 0.1em; text-align: center; color: black; font-weight: bold;"><a href="/wiki/%D7%AA%D7%91%D7%A0%D7%99%D7%AA:%D7%A2%D7%A5_%D7%9E%D7%99%D7%95%D7%9F_%D7%A9%D7%9C_%D7%9E%D7%A8%D7%97%D7%91%D7%99%D7%9D_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%99%D7%9D_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%99%D7%9D" title="תבנית:עץ מיון של מרחבים וקטוריים טופולוגיים">עץ מיון של מרחבים וקטוריים טופולוגיים</a> </th></tr> <tr> <td style="padding-top: 3px; padding-bottom: 3px; background-color: #f9f9f9; font-size: 95%"> <table style="width: 98%; background-color: transparent; margin: auto; padding: 0; text-align: right;" cellpadding="0" cellspacing="0"> <tbody><tr> <td><div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r40000942"> <table class="DiagramTable"> <tbody><tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב וקטורי טופולוגי">מרחב וקטורי טופולוגי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב וקטורי טופולוגי">מרחב וקטורי טופולוגי</a></div> <div class="Diagram3"></div> </div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="6" rowspan="5"><div style="position: relative; vertical-align:top; text-align: right; justify-content: center; align-items: center; padding: 5px; border: 2px solid black; border-radius: 5px; background-color: white; right:20px; width:calc(100% - 50px)"><b>מקרא:</b> <table class="DiagramLegend"> <tbody><tr> <td><span style="display:inline-block; border:2px solid black; vertical-align:text-top; border-radius:5px ;" title="#FFFFBE"><span style="display:block; padding:0; width:calc(1em * 1); height:1em ; background: #FFFFBE; border-radius:calc(5px - 2px );"> </span></span> </td> <td>מחלקה של מרחבים וקטוריים טופולוגיים (מעל <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span></a>).<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span style="display:inline-block; border:2px solid #78A6A6; vertical-align:text-top; border-radius:5px ;" title="#BEFFFF"><span style="display:block; padding:0; width:calc(1em * 1); height:1em ; background: #BEFFFF; border-radius:calc(5px - 2px );"> </span></span> </td> <td>דוגמה או קבוצת דוגמאות למרחבים וקטוריים טופולוגיים.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </td></tr> <tr> <td><span style="display:inline-block; border-top:2px solid black; vertical-align:middle;"><span style="display:block; padding:0; width:1em ; height:0;"> </span></span> </td> <td>מסלול שיורד למטה מצביע על כך שהמחלקה התחתונה היא חלק מהמחלקה העליונה. </td></tr> <tr> <td><span style="display:inline-block; border-top:2px solid #78A6A6; vertical-align:middle;"><span style="display:block; padding:0; width:1em ; height:0;"> </span></span> </td> <td>חלק במסלול שרלוונטי רק לדוגמאות. </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d4e886e6f5a28a33e073fb108440c152ecfe2d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \cap }"></span> </td> <td><span id="חיתוך" class="citation">מחלקה המהווה <a href="/wiki/%D7%97%D7%99%D7%AA%D7%95%D7%9A_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="חיתוך (מתמטיקה)">חיתוך</a> של המחלקות שמכילות אותה ומופיעות בתרשים.</span> </td></tr></tbody></table></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%90%D7%95%D7%A1%D7%93%D7%95%D7%A8%D7%A3" title="מרחב האוסדורף">האוסדורף</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%90%D7%95%D7%A1%D7%93%D7%95%D7%A8%D7%A3" title="מרחב האוסדורף">האוסדורף</a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td></tr> <tr><td></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99%D7%96%D7%91%D7%99%D7%9C%D7%99" title="מרחב מטריזבילי">מטריזבילי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99%D7%96%D7%91%D7%99%D7%9C%D7%99" title="מרחב מטריזבילי">מטריזבילי</a></div> <div class="Diagram3"></div> </div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A9%D7%9C%D7%9D" class="mw-redirect" title="מרחב שלם">שלם</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A9%D7%9C%D7%9D" class="mw-redirect" title="מרחב שלם">שלם</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A7%D7%9E%D7%95%D7%A8_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA" title="מרחב קמור מקומית">מרחב קמור מקומית</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A7%D7%9E%D7%95%D7%A8_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA" title="מרחב קמור מקומית">מרחב קמור מקומית</a></div> <div class="Diagram3"></div> </div></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 4px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 4px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 4px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - -2px ); height:50%; border-top: 2px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 0px); border-left: 0px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid black; border-bottom: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - -2px ); height:50%; border-top: 0px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91-F&action=edit&redlink=1" class="new" title="מרחב-F (הדף אינו קיים)">מרחב-F</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91-F&action=edit&redlink=1" class="new" title="מרחב-F (הדף אינו קיים)">מרחב-F</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td>                              </td></tr> <tr><td></td><td></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr> <tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A8%D7%A0%D7%94_%D7%9E%D7%95%D7%A8%D7%99%D7%A1_%D7%A4%D7%A8%D7%A9%D7%94" title="רנה מוריס פרשה"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/75px-Frechet.jpeg" decoding="async" width="75" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/113px-Frechet.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/150px-Frechet.jpeg 2x" data-file-width="268" data-file-height="326" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב פרשה (הדף אינו קיים)">מרחב פרשה</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A8%D7%A0%D7%94_%D7%9E%D7%95%D7%A8%D7%99%D7%A1_%D7%A4%D7%A8%D7%A9%D7%94" title="רנה מוריס פרשה"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/75px-Frechet.jpeg" decoding="async" width="75" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/113px-Frechet.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a5/Frechet.jpeg/150px-Frechet.jpeg 2x" data-file-width="268" data-file-height="326" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב פרשה (הדף אינו קיים)">מרחב פרשה</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%93%D7%95%D7%90%D7%9C%D7%99_%D7%9C%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב דואלי לפרשה (הדף אינו קיים)">מרחב דואלי לפרשה</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%93%D7%95%D7%90%D7%9C%D7%99_%D7%9C%D7%A4%D7%A8%D7%A9%D7%94&action=edit&redlink=1" class="new" title="מרחב דואלי לפרשה (הדף אינו קיים)">מרחב דואלי לפרשה</a></div> <div class="Diagram3"></div> </div></td><td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%90%D7%9C%D7%9B%D7%A1%D7%A0%D7%93%D7%A8_%D7%92%D7%A8%D7%95%D7%98%D7%A0%D7%93%D7%99%D7%A7" title="אלכסנדר גרוטנדיק"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/75px-Alexander_Grothendieck_-_face.jpg" decoding="async" width="75" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/113px-Alexander_Grothendieck_-_face.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/150px-Alexander_Grothendieck_-_face.jpg 2x" data-file-width="156" data-file-height="198" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%92%D7%A8%D7%A2%D7%99%D7%A0%D7%99&action=edit&redlink=1" class="new" title="מרחב גרעיני (הדף אינו קיים)">מרחב גרעיני</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%90%D7%9C%D7%9B%D7%A1%D7%A0%D7%93%D7%A8_%D7%92%D7%A8%D7%95%D7%98%D7%A0%D7%93%D7%99%D7%A7" title="אלכסנדר גרוטנדיק"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/75px-Alexander_Grothendieck_-_face.jpg" decoding="async" width="75" height="95" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/113px-Alexander_Grothendieck_-_face.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Alexander_Grothendieck_-_face.jpg/150px-Alexander_Grothendieck_-_face.jpg 2x" data-file-width="156" data-file-height="198" /></a><figcaption></figcaption></figure><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%92%D7%A8%D7%A2%D7%99%D7%A0%D7%99&action=edit&redlink=1" class="new" title="מרחב גרעיני (הדף אינו קיים)">מרחב גרעיני</a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c913ced284ad05bd42c8f004a3a83dee6323cb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c913ced284ad05bd42c8f004a3a83dee6323cb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%99" title="מרחב נורמי">מרחב נורמי</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%99" title="מרחב נורמי">מרחב נורמי</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 0px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:1;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:1;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - calc(-2px * 2) - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td></tr><tr><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A1%D7%98%D7%A4%D7%9F_%D7%91%D7%A0%D7%9A" title="סטפן בנך"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/75px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg" decoding="async" width="75" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/113px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/150px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 2x" data-file-width="348" data-file-height="467" /></a><figcaption></figcaption></figure><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A" title="מרחב בנך">מרחב בנך</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%A1%D7%98%D7%A4%D7%9F_%D7%91%D7%A0%D7%9A" title="סטפן בנך"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/75px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg" decoding="async" width="75" height="101" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/113px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg/150px-Stefana_Banach_-_%D8%B3%D8%AA%D9%8A%D9%81%D8%A7%D9%86_%D8%A8%D9%86%D8%A7%D8%AE.jpg 2x" data-file-width="348" data-file-height="467" /></a><figcaption></figcaption></figure><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A" title="מרחב בנך">מרחב בנך</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dfc074a50ce00ca95d3dc94ebae8432e2949a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.337ex; height:3.176ex;" alt="{\displaystyle C^{-\infty }(S^{1})}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66dfc074a50ce00ca95d3dc94ebae8432e2949a4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.337ex; height:3.176ex;" alt="{\displaystyle C^{-\infty }(S^{1})}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94-Lp_%D7%91%D7%90%D7%95%D7%A4%D7%9F_%D7%9E%D7%A7%D7%95%D7%9E%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות ה-Lp באופן מקומי (הדף אינו קיים)"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{loc}^{p}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3b8f175d94399b4ef7a4ea13f6206fc06227d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.302ex; height:3.176ex;" alt="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94-Lp_%D7%91%D7%90%D7%95%D7%A4%D7%9F_%D7%9E%D7%A7%D7%95%D7%9E%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות ה-Lp באופן מקומי (הדף אינו קיים)"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>l</mi> <mi>o</mi> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{loc}^{p}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cc3b8f175d94399b4ef7a4ea13f6206fc06227d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.302ex; height:3.176ex;" alt="{\displaystyle L_{loc}^{p}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c83d1af403f8fe4ad3b88bf35451369497d8c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.254ex; height:2.843ex;" alt="{\displaystyle C(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7c83d1af403f8fe4ad3b88bf35451369497d8c9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.254ex; height:2.843ex;" alt="{\displaystyle C(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr><tr><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 3px + 2px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 3px ); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -4px - 1 * 2px); border-left: 2px solid black; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 0px - 0.5 * 2px); border-left: 2px solid black; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA_%D7%91%D7%A2%D7%9C%D7%95%D7%AA_%D7%AA%D7%95%D7%9E%D7%9A_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות בעלות תומך קומפקטי (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{c}^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbf3b0bd3006d257867fee68628fcdd300e2f04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%97%D7%9C%D7%A7%D7%95%D7%AA_%D7%91%D7%A2%D7%9C%D7%95%D7%AA_%D7%AA%D7%95%D7%9E%D7%9A_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99&action=edit&redlink=1" class="new" title="מרחב הפונקציות החלקות בעלות תומך קומפקטי (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{c}^{\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbbf3b0bd3006d257867fee68628fcdd300e2f04" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.161ex; height:2.843ex;" alt="{\displaystyle C_{c}^{\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"></td></tr><tr><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94_%D7%A4%D7%A0%D7%99%D7%9E%D7%99%D7%AA" title="מרחב מכפלה פנימית">מרחב מכפלה פנימית</a></div> <div class="Diagram3"></div> </div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid black; border-top: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval4" style="right: calc(50% + -2px + 0px); height:50%; border-top: 0px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:1;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - -2px - 1 * 2px); border-left: 2px solid black; z-index:1;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - -4px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr> <tr><td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div class="interval46" style="border-top: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td><div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td> <td colspan="3" rowspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%93%D7%95%D7%93_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="דוד הילברט"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/75px-Hilbert.jpg" decoding="async" width="75" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/113px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/150px-Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption></figcaption></figure><a class="mw-selflink selflink">מרחב הילברט</a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><figure class="mw-halign-center" typeof="mw:File"><a href="/wiki/%D7%93%D7%95%D7%93_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="דוד הילברט"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/75px-Hilbert.jpg" decoding="async" width="75" height="102" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/113px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/150px-Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption></figcaption></figure><a class="mw-selflink selflink">מרחב הילברט</a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9463391c47586860b3c88f37dc709ebbcefd5a20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.439ex; height:3.009ex;" alt="{\displaystyle C^{-\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%9E%D7%95%D7%9B%D7%9C%D7%9C%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות המוכללות (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C^{-\infty }(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C^{-\infty }(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9463391c47586860b3c88f37dc709ebbcefd5a20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.439ex; height:3.009ex;" alt="{\displaystyle C^{-\infty }(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td> <td></td> <td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr><tr><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L1" class="mw-redirect" title="מרחב L1"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{1}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{1}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a86223fba658a5daf612b39d3e25495d548bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{1}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L1" class="mw-redirect" title="מרחב L1"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{1}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{1}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9a86223fba658a5daf612b39d3e25495d548bdb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{1}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aecdea502af56c65e0d42c2e477eba765beefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.152ex; height:3.176ex;" alt="{\displaystyle C(S^{1})}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%AA_%D7%94%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA_%D7%A2%D7%9C_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98&action=edit&redlink=1" class="new" title="מרחב הפונקציות הרציפות על קומפקט (הדף אינו קיים)"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C(S^{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>C</mi> <mo stretchy="false">(</mo> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C(S^{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97aecdea502af56c65e0d42c2e477eba765beefd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.152ex; height:3.176ex;" alt="{\displaystyle C(S^{1})}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid #78A6A6; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td></td><td><div style="content: ''; position: absolute; bottom: 0; left: 0; right: calc(50% + 0px); height:calc(50% - 0px); border-radius: 0 10px 0 0 ; border-right: 0px solid black; border-top: 0px solid black;"></div> <div style="content: ''; position: absolute; bottom: 0; right: 0; width: calc(50% - 0px); height:calc(50% - 0px); border-radius: 10px 0 0 0 ; border-left: 2px solid #78A6A6; border-top: 2px solid #78A6A6;"></div> <div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div> <div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 0px solid black; border-bottom: 0px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_Lp" title="מרחב Lp"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{p}(\mathbb {R} );p>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> <mo>;</mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{p}(\mathbb {R} );p>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e5b46d45a471a76e8e5c35bde8a6775cec087d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.594ex; height:2.843ex;" alt="{\displaystyle L^{p}(\mathbb {R} );p>1}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_Lp" title="מרחב Lp"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{p}(\mathbb {R} );p>1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> <mo>;</mo> <mi>p</mi> <mo>></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{p}(\mathbb {R} );p>1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e5b46d45a471a76e8e5c35bde8a6775cec087d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.594ex; height:2.843ex;" alt="{\displaystyle L^{p}(\mathbb {R} );p>1}"></span></a></div> <div class="Diagram3"></div> </div></td><td></td><td></td><td><div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td><td></td><td></td><td></td></tr><tr><td></td><td></td> <td></td> <td></td> <td></td> <td></td> <td><div class="interval4" style="right: calc(50% + 0px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval28" style="border-left: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 3px - 1 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 3px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval4" style="right: calc(50% + -2px + 2px); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval6" style="width: calc(50% - 0px ); height:50%; border-top: 2px solid black; z-index:0;"> </div> <div class="interval8" style="width: 50%; height:calc(100% - 50% - 3px - 1 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div> <div class="interval2" style="width: 50%; height:calc(50% + 0.5 * 2px - 3px - 0.5 * 2px); border-left: 2px solid #78A6A6; z-index:0;"> </div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div class="interval46" style="border-top: 2px solid black; z-index:0;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td><div style="content: ''; position: absolute; top: 0; right: 0; width: calc(50% - 0px); bottom: calc(50% + 0px); border-radius: 0 0 0 10px ; border-left: 2px solid black; border-bottom: 2px solid black;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td><td></td><td></td></tr> <tr><td></td><td></td><td></td><td></td><td></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #FFFFBE; z-index:-1; border: 2px solid black; padding-top:1.2em; padding-bottom:1.2em;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> (<a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים">ממשי</a>) <a href="/wiki/%D7%9E%D7%9E%D7%93_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="ממד (אלגברה ליניארית)">ממד</a> סופי - <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid black; border-radius: 5px ; background-color: #FFFFBE;"> <div class="Diagram2" style="padding-top:1.2em; padding-bottom:1.2em; width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99" title="מרחב וקטורי">מרחב</a> (<a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים">ממשי</a>) <a href="/wiki/%D7%9E%D7%9E%D7%93_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99%D7%AA)" title="ממד (אלגברה ליניארית)">ממד</a> סופי - <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A7%D7%9C%D7%99%D7%93%D7%99" title="מרחב אוקלידי"> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} ^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} ^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c510b63578322050121fe966f2e5770bea43308d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.897ex; height:2.343ex;" alt="{\displaystyle \mathbb {R} ^{n}}"></span></a></div> <div class="Diagram3"><a href="#חיתוך"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cap \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∩</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cap \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/051a280b6249172dae82ae57360a625c47cb57ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.937ex; height:2.009ex;" alt="{\displaystyle \cap \,}"></span></a></div> </div></td> <td><div style="content: ''; position: absolute; top: 0; left: 0; bottom: calc(50% + 0px); right: calc(50% + 0px); border-radius: 0 0 10px 0 ; border-right: 2px solid #78A6A6; border-bottom: 2px solid #78A6A6;"></div><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td colspan="3"> <div style="width: 100%; min-height:100%; vertical-align: middle; justify-content: center; align-items: center; padding: 2px; box-sizing: border-box; top:0; left:0; border-radius: 5px ; background-color: #BEFFFF; z-index:-1; border: 2px solid #78A6A6;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L2" class="mw-redirect" title="מרחב L2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8722fb232f689925a4baa0e4ba478e43ee346672" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{2}(\mathbb {R} )}"></span></a></div> <div class="Diagram1" style="vertical-align: middle; left:0; min-height:100%; justify-content: center; align-items: center; border: 2px solid #78A6A6; border-radius: 5px ; background-color: #BEFFFF;"> <div class="Diagram2" style="width: 100%;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_L2" class="mw-redirect" title="מרחב L2"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L^{2}(\mathbb {R} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L^{2}(\mathbb {R} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8722fb232f689925a4baa0e4ba478e43ee346672" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.124ex; height:3.176ex;" alt="{\displaystyle L^{2}(\mathbb {R} )}"></span></a></div> <div class="Diagram3"></div> </div></td> <td><div style="width: 2em ; height: 2em ;"><span style="font: 1px/1px serif;"> </span></div></td> <td></td> <td></td> <td></td><td></td><td></td></tr> </tbody></table></div> <div class="reflist references-small"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">^</a></span> <span class="reference-text">שמות התואר "וקטורי", "טופולוגי" ו"ממשי" מושמטים בדרך כלל משם המחלקה.</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">^</a></span> <span class="reference-text">במרחבי הפונקציות בדוגמאות, ניתן להחליף את <a href="/wiki/%D7%A9%D7%93%D7%94_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D_%D7%94%D7%9E%D7%9E%D7%A9%D7%99%D7%99%D7%9D" title="שדה המספרים הממשיים"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span></a> ב<a href="/wiki/%D7%99%D7%A8%D7%99%D7%A2%D7%94_%D7%97%D7%9C%D7%A7%D7%94" title="יריעה חלקה">יריעה חלקה</a> כלשהי ואת מעגל היחידה <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S^{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S^{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/60796c8d0c03cf575637d3202463b214d9635880" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.576ex; height:2.676ex;" alt="{\displaystyle S^{1}}"></span> ביריעה חלקה <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%AA" title="קבוצה קומפקטית">קומפקטית</a> כלשהי.</span> </li> </ol></div></div> </td></tr></tbody></table> </td></tr></tbody></table> </div> <p><br /> </p> <div role="navigation" class="navbox authority-control" aria-labelledby="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q190056?uselang=he&#124;עריכת_הנתון_בוויקינתונים" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="בקרת_זהויות_15px&#124;link=https&#58;//www.wikidata.org/wiki/Q190056?uselang=he&#124;עריכת_הנתון_בוויקינתונים" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%D7%A2%D7%96%D7%A8%D7%94:%D7%91%D7%A7%D7%A8%D7%AA_%D7%96%D7%94%D7%95%D7%99%D7%95%D7%AA" title="עזרה:בקרת זהויות">בקרת זהויות</a> <span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q190056?uselang=he" title="עריכת הנתון בוויקינתונים"><img alt="עריכת הנתון בוויקינתונים" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/15px-Blue_pencil_RTL.svg.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/23px-Blue_pencil_RTL.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5e/Blue_pencil_RTL.svg/30px-Blue_pencil_RTL.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></th><td class="navbox-list navbox-odd" style="text-align:left;border-right-width:2px;border-right-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><div dir="ltr"> <ul><li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="הספרייה הלאומית">NLI</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007560453005171">987007560453005171</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A1%D7%A4%D7%A8%D7%93" title="הספרייה הלאומית של ספרד">BNE</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://catalogo.bne.es/uhtbin/authoritybrowse.cgi?action=display&authority_id=XX531621">XX531621</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A6%D7%A8%D7%A4%D7%AA" title="הספרייה הלאומית של צרפת">BnF</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb11979628h">cb11979628h</a> <a rel="nofollow" class="external text" href="https://data.bnf.fr/ark:/12148/cb11979628h">(data)</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A7%D7%95%D7%91%D7%A5_%D7%91%D7%A7%D7%A8%D7%94_%D7%9E%D7%A9%D7%95%D7%9C%D7%91" title="קובץ בקרה משולב">GND</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4159850-7">4159850-7</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A9%D7%99%D7%98%D7%AA_%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%AA_%D7%94%D7%A7%D7%95%D7%A0%D7%92%D7%A8%D7%A1" title="שיטת ספריית הקונגרס">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/subjects/sh85060803">sh85060803</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%AA_%D7%94%D7%93%D7%99%D7%90%D7%98_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA" title="ספריית הדיאט הלאומית">NDL</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00563198">00563198</a></span></span></li> <li><span class="nowrap"><a href="/wiki/%D7%94%D7%A1%D7%A4%D7%A8%D7%99%D7%99%D7%94_%D7%94%D7%9C%D7%90%D7%95%D7%9E%D7%99%D7%AA_%D7%A9%D7%9C_%D7%A6%27%D7%9B%D7%99%D7%94" title="הספרייה הלאומית של צ'כיה">NKC</a>: <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph117602&CON_LNG=ENG">ph117602</a></span></span></li></ul> </div></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">אוחזר מתוך "<a dir="ltr" href="https://he.wikipedia.org/w/index.php?title=מרחב_הילברט&oldid=39850545">https://he.wikipedia.org/w/index.php?title=מרחב_הילברט&oldid=39850545</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D7%95%D7%99%D7%A7%D7%99%D7%A4%D7%93%D7%99%D7%94:%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94" title="ויקיפדיה:קטגוריה">קטגוריות</a>: <ul><li><a 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