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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%91%D7%A0%D7%9A" 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%91%D7%A0%D7%9A" 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> 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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-תכונות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#תכונות"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>תכונות</span> </div> </a> <ul id="toc-תכונות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-דוגמאות" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#דוגמאות"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>דוגמאות</span> </div> </a> <button aria-controls="toc-דוגמאות-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 דוגמאות</span> </button> <ul id="toc-דוגמאות-sublist" class="vector-toc-list"> <li id="toc-מרחבי_סדרות" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#מרחבי_סדרות"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>מרחבי סדרות</span> </div> </a> <ul id="toc-מרחבי_סדרות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-מרחבי_פונקציות" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#מרחבי_פונקציות"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>מרחבי פונקציות</span> </div> </a> <ul id="toc-מרחבי_פונקציות-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-טיפוסים_של_מרחבי_בנך" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#טיפוסים_של_מרחבי_בנך"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>טיפוסים של מרחבי בנך</span> </div> </a> <ul id="toc-טיפוסים_של_מרחבי_בנך-sublist" class="vector-toc-list"> </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">4</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">5</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">5.1</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 בנך</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־41 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-41" 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">41 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 mw-list-item"><a href="https://en.wikipedia.org/wiki/Banach_space" title="Banach space – אנגלית" lang="en" hreflang="en" data-title="Banach space" data-language-autonym="English" data-language-local-name="אנגלית" class="interlanguage-link-target"><span>English</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_%D8%A8%D8%A7%D9%86%D8%A7%D8%AE" title="فضاء باناخ – ערבית" lang="ar" hreflang="ar" data-title="فضاء باناخ" data-language-autonym="العربية" data-language-local-name="ערבית" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%A8%D8%A7%D9%86%D8%A7%D8%AE_%D8%A7%DB%87%D8%B2%D8%A7%DB%8C%DB%8C" title="باناخ اۇزایی – אזרבייג׳נית דרומית" lang="azb" hreflang="azb" data-title="باناخ اۇزایی" data-language-autonym="تۆرکجه" data-language-local-name="אזרבייג׳נית דרומית" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B0%D0%BD%D0%B0%D1%85%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="Банахово пространство – בולגרית" lang="bg" hreflang="bg" data-title="Банахово пространство" data-language-autonym="Български" data-language-local-name="בולגרית" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Espai_de_Banach" title="Espai de Banach – קטלאנית" lang="ca" hreflang="ca" data-title="Espai de Banach" 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_%D8%A8%D8%A7%D9%86%D8%A7%D8%AE" title="بۆشاییی باناخ – כורדית סוראנית" lang="ckb" hreflang="ckb" data-title="بۆشاییی باناخ" 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/Banach%C5%AFv_prostor" title="Banachův prostor – צ׳כית" lang="cs" hreflang="cs" data-title="Banachův 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-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Banachraum" title="Banachraum – גרמנית" lang="de" hreflang="de" data-title="Banachraum" 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%9C%CF%80%CE%AC%CE%BD%CE%B1%CF%87" title="Χώρος Μπάναχ – יוונית" lang="el" hreflang="el" data-title="Χώρος Μπάναχ" 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/Bana%C4%A5a_spaco" title="Banaĥa spaco – אספרנטו" lang="eo" hreflang="eo" data-title="Banaĥa 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_Banach" title="Espacio de Banach – ספרדית" lang="es" hreflang="es" data-title="Espacio de Banach" 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/Banachi_ruum" title="Banachi ruum – אסטונית" lang="et" hreflang="et" data-title="Banachi ruum" data-language-autonym="Eesti" data-language-local-name="אסטונית" class="interlanguage-link-target"><span>Eesti</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_%D8%A8%D8%A7%D9%86%D8%A7%D8%AE" title="فضای باناخ – פרסית" lang="fa" hreflang="fa" data-title="فضای باناخ" 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/Banachin_avaruus" title="Banachin avaruus – פינית" lang="fi" hreflang="fi" data-title="Banachin 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_Banach" title="Espace de Banach – צרפתית" lang="fr" hreflang="fr" data-title="Espace de Banach" data-language-autonym="Français" data-language-local-name="צרפתית" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Banach-t%C3%A9r" title="Banach-tér – הונגרית" lang="hu" hreflang="hu" data-title="Banach-tér" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ruang_Banach" title="Ruang Banach – אינדונזית" lang="id" hreflang="id" data-title="Ruang Banach" 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/Banach-r%C3%BAm" title="Banach-rúm – איסלנדית" lang="is" hreflang="is" data-title="Banach-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_Banach" title="Spazio di Banach – איטלקית" lang="it" hreflang="it" data-title="Spazio di Banach" 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%90%E3%83%8A%E3%83%83%E3%83%8F%E7%A9%BA%E9%96%93" title="バナッハ空間 – יפנית" lang="ja" hreflang="ja" data-title="バナッハ空間" 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-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D0%B0%D0%BD%D0%B0%D1%85_%D0%BA%D0%B5%D2%A3%D1%96%D1%81%D1%82%D1%96%D0%B3%D1%96" title="Банах кеңістігі – קזחית" lang="kk" hreflang="kk" data-title="Банах кеңістігі" data-language-autonym="Қазақша" data-language-local-name="קזחית" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B2%BE%E0%B2%A8%E0%B2%BE%E0%B2%95%E0%B3%8D_%E0%B2%86%E0%B2%95%E0%B2%BE%E0%B2%B6" title="ಬಾನಾಕ್ ಆಕಾಶ – קנאדה" lang="kn" hreflang="kn" data-title="ಬಾನಾಕ್ ಆಕಾಶ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="קנאדה" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%94%EB%82%98%ED%9D%90_%EA%B3%B5%EA%B0%84" title="바나흐 공간 – קוריאנית" lang="ko" hreflang="ko" data-title="바나흐 공간" data-language-autonym="한국어" data-language-local-name="קוריאנית" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Banachruimte" title="Banachruimte – הולנדית" lang="nl" hreflang="nl" data-title="Banachruimte" 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/Banachrom" title="Banachrom – נורווגית חדשה" lang="nn" hreflang="nn" data-title="Banachrom" 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/Banach-rom" title="Banach-rom – נורווגית ספרותית" lang="nb" hreflang="nb" data-title="Banach-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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przestrze%C5%84_Banacha" title="Przestrzeń Banacha – פולנית" lang="pl" hreflang="pl" data-title="Przestrzeń Banacha" data-language-autonym="Polski" data-language-local-name="פולנית" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Spassi_%C3%ABd_Banach" title="Spassi ëd Banach – פיימונטית" lang="pms" hreflang="pms" data-title="Spassi ëd Banach" data-language-autonym="Piemontèis" data-language-local-name="פיימונטית" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Espa%C3%A7o_de_Banach" title="Espaço de Banach – פורטוגזית" lang="pt" hreflang="pt" data-title="Espaço de Banach" 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_Banach" title="Spațiu Banach – רומנית" lang="ro" hreflang="ro" data-title="Spațiu Banach" 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%91%D0%B0%D0%BD%D0%B0%D1%85%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="Банахово пространство – רוסית" lang="ru" hreflang="ru" data-title="Банахово пространство" data-language-autonym="Русский" data-language-local-name="רוסית" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Banach_space" title="Banach space – אנגלית פשוטה" lang="en-simple" hreflang="en-simple" data-title="Banach 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/Banachov_priestor" title="Banachov priestor – סלובקית" lang="sk" hreflang="sk" data-title="Banachov 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/Banachov_prostor" title="Banachov prostor – סלובנית" lang="sl" hreflang="sl" data-title="Banachov prostor" data-language-autonym="Slovenščina" data-language-local-name="סלובנית" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Banachrum" title="Banachrum – שוודית" lang="sv" hreflang="sv" data-title="Banachrum" data-language-autonym="Svenska" data-language-local-name="שוודית" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Banach_uzay%C4%B1" title="Banach uzayı – טורקית" lang="tr" hreflang="tr" data-title="Banach 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%91%D0%B0%D0%BD%D0%B0%D1%85%D1%96%D0%B2_%D0%BF%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80" title="Банахів простір – אוקראינית" lang="uk" hreflang="uk" data-title="Банахів простір" data-language-autonym="Українська" data-language-local-name="אוקראינית" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Kh%C3%B4ng_gian_Banach" title="Không gian Banach – וייטנאמית" lang="vi" hreflang="vi" data-title="Không gian Banach" 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%B7%B4%E6%8B%BF%E8%B5%AB%E7%A9%BA%E9%97%B4" title="巴拿赫空间 – סינית וו" lang="wuu" hreflang="wuu" data-title="巴拿赫空间" 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%B7%B4%E6%8B%BF%E8%B5%AB%E7%A9%BA%E9%97%B4" title="巴拿赫空间 – סינית" lang="zh" hreflang="zh" data-title="巴拿赫空间" 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-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%B7%B4%E6%8B%BF%E8%B5%AB%E7%A9%BA%E9%96%93" title="巴拿赫空間 – קנטונזית" lang="yue" hreflang="yue" data-title="巴拿赫空間" 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/Q194397#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%91%D7%A0%D7%9A" 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%91%D7%A0%D7%9A" rel="discussion" title="שיחה על דף התוכן [t]" 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data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">כלים</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">העברה לסרגל הצד</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">הסתרה</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="אפשרויות נוספות" > <div class="vector-menu-heading"> פעולות </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A"><span>קריאה</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A&action=edit" title="עריכת קוד המקור של הדף הזה [e]" accesskey="e"><span>עריכת קוד מקור</span></a></li><li id="ca-more-ve-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%A0%D7%9A&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%91%D7%A0%D7%9A&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%91%D7%A0%D7%9A" 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%91%D7%A0%D7%9A" 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%91%D7%A0%D7%9A&oldid=39850689" 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%91%D7%A0%D7%9A&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%91%D7%A0%D7%9A&id=39850689&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%2591%25D7%25A0%25D7%259A"><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%2591%25D7%25A0%25D7%259A"><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%91%D7%A0%D7%9A"><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%91%D7%A0%D7%9A&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%91%D7%A0%D7%9A&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:Banach_spaces" 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/Q194397" 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>ב<a href="/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="מתמטיקה">מתמטיקה</a>, <b>מרחב בנך</b> (ב<a href="/wiki/%D7%90%D7%A0%D7%92%D7%9C%D7%99%D7%AA" title="אנגלית">אנגלית</a>: Banach space) 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> <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%99" title="מרחב נורמי">נורמי</a> שהוא <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> ב<a href="/wiki/%D7%9E%D7%98%D7%A8%D7%99%D7%A7%D7%94" title="מטריקה">מטריקה</a> <a href="/w/index.php?title=%D7%94%D7%A9%D7%A8%D7%90%D7%94_(%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94)&action=edit&redlink=1" class="new" title="השראה (אנליזה) (הדף אינו קיים)">המושרית</a> מן 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>. מרחב בנך הוא אחד המרחבים הנפוצים שנחקרים במסגרת ה<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>. </p><p>מרחב בנך נקרא על שם <a href="/wiki/%D7%A1%D7%98%D7%A4%D7%9F_%D7%91%D7%A0%D7%9A" title="סטפן בנך">סטפן בנך</a>, <a href="/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%90%D7%99" title="מתמטיקאי">מתמטיקאי</a> <a href="/wiki/%D7%A4%D7%95%D7%9C%D7%99%D7%9F" title="פולין">פולני</a> שהיה מבין מייסדי התחום וממנסחי משפטיו היסודיים. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="תכונות"><span id=".D7.AA.D7.9B.D7.95.D7.A0.D7.95.D7.AA"></span>תכונות</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%91%D7%A0%D7%9A&action=edit&section=1" title="עריכת קוד המקור של הפרק: תכונות"><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%91%D7%A0%D7%9A&veaction=edit&section=1" title="עריכת פסקה: "תכונות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D7%9B%D7%93%D7%95%D7%A8_%D7%99%D7%97%D7%99%D7%93%D7%94" class="mw-redirect" title="כדור יחידה">כדור היחידה</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 \ \{x:||x||<1\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo fence="false" stretchy="false">{</mo> <mi>x</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mn>1</mn> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \{x:||x||<1\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4d0a119ad9e41fa1e26cf0a6923b9cba966302c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.35ex; height:2.843ex;" alt="{\displaystyle \ \{x:||x||<1\}}"></span> במרחב נורמי הוא תמיד <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A7%D7%9E%D7%95%D7%A8%D7%94" title="קבוצה קמורה">קמור</a>, <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A4%D7%AA%D7%95%D7%97%D7%94" title="קבוצה פתוחה">פתוח</a> ו<a href="/wiki/%D7%A1%D7%99%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="סימטריה">סימטרי</a> לשיקוף סביב 0. במרחב ממימד סופי, גם ההפך נכון: כל גוף בעל פנים לא ריק בעל תכונות אלה הוא כדור היחידה של נורמה מתאימה. התנאי על קמירות כדור היחידה שקול ל<a href="/wiki/%D7%90%D7%99-%D7%A9%D7%95%D7%95%D7%99%D7%95%D7%9F_%D7%94%D7%9E%D7%A9%D7%95%D7%9C%D7%A9" title="אי-שוויון המשולש">אי-שוויון המשולש</a> שהנורמה צריכה לקיים. </p><p><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%90%D7%9F-%D7%91%D7%A0%D7%9A" title="משפט האן-בנך">משפט האן-בנך</a> מאפשר להרחיב פונקציונלים מתת-מרחב אל המרחב כולו, וכך מאפשר לבנות פונקציונלים רציפים רבים. </p><p><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%91%D7%A0%D7%9A-%D7%A9%D7%98%D7%99%D7%99%D7%A0%D7%94%D7%90%D7%95%D7%A1" title="משפט בנך-שטיינהאוס">משפט בנך-שטיינהאוס</a> (הנקרא גם עקרון החסימות במידה שווה) טוען שאם למשפחה של <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8" title="אופרטור">אופרטורים</a> <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">ליניאריים</a> <a href="/wiki/%D7%A8%D7%A6%D7%99%D7%A4%D7%95%D7%AA" class="mw-redirect" title="רציפות">רציפים</a> על מרחב בנך יש חסם משותף בכל נקודה של המרחב, אז יש חסם אחיד על ה<a href="/wiki/%D7%A0%D7%95%D7%A8%D7%9E%D7%94_%D7%A9%D7%9C_%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8" title="נורמה של אופרטור">נורמה</a> שלהם. </p><p>לפי <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%94%D7%A2%D7%AA%D7%A7%D7%94_%D7%94%D7%A4%D7%AA%D7%95%D7%97%D7%94" title="משפט ההעתקה הפתוחה">משפט ההעתקה הפתוחה</a> (או בניסוח שקול <a href="/w/index.php?title=%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%92%D7%A8%D7%A3_%D7%94%D7%A1%D7%92%D7%95%D7%A8&action=edit&redlink=1" class="new" title="משפט הגרף הסגור (הדף אינו קיים)">משפט הגרף הסגור</a>), כל <a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8_%D7%9C%D7%99%D7%A0%D7%99%D7%90%D7%A8%D7%99_%D7%97%D7%A1%D7%95%D7%9D" title="אופרטור ליניארי חסום">אופרטור ליניארי חסום</a> ממרחב בנך אחד על מרחב בנך אחר, הוא פתוח. </p><p>לפי <a href="/w/index.php?title=%D7%9E%D7%A9%D7%A4%D7%98_%D7%9E%D7%96%D7%95%D7%A8-%D7%90%D7%95%D7%9C%D7%9D&action=edit&redlink=1" class="new" title="משפט מזור-אולם (הדף אינו קיים)">משפט מזור-אולם</a>, המבנה המטרי על מרחב בנך קובע את המבנה הליניארי שלו: 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 \ f:X\to Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>f</mi> <mo>:</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ f:X\to Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fc5c3c66b376ba791d22d1493dbdb3b0aebe91a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.164ex; height:2.509ex;" alt="{\displaystyle \ f:X\to Y}"></span> היא <a href="/wiki/%D7%90%D7%99%D7%96%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%94" title="איזומטריה">איזומטריה</a> בין מרחבי בנך וגם על, אז <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"> <mtext> </mtext> <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/4d5ff7312a01506eee6ecea7dca662763a101c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.859ex; height:2.509ex;" alt="{\displaystyle \ f}"></span> היא ליניארית. </p> <div class="mw-heading mw-heading2"><h2 id="דוגמאות"><span id=".D7.93.D7.95.D7.92.D7.9E.D7.90.D7.95.D7.AA"></span>דוגמאות</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%91%D7%A0%D7%9A&action=edit&section=2" title="עריכת קוד המקור של הפרק: דוגמאות"><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%91%D7%A0%D7%9A&veaction=edit&section=2" title="עריכת פסקה: "דוגמאות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><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">המרחב האוקלידי</a> הוא מרחב בנך. באופן כללי יותר, כל <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">מרחב הילברט</a> הוא מרחב בנך.</li></ul> <div class="mw-heading mw-heading3"><h3 id="מרחבי_סדרות"><span id=".D7.9E.D7.A8.D7.97.D7.91.D7.99_.D7.A1.D7.93.D7.A8.D7.95.D7.AA"></span>מרחבי סדרות</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%91%D7%A0%D7%9A&action=edit&section=3" title="עריכת קוד המקור של הפרק: מרחבי סדרות"><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%91%D7%A0%D7%9A&veaction=edit&section=3" title="עריכת פסקה: "מרחבי סדרות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>אוסף הסדרות של מספרים ממשיים <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 \ (a_{n})_{n\in \mathbb {N} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <msub> <mi>a</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> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (a_{n})_{n\in \mathbb {N} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbef5de6febc60de99017922f0f44fdd83d516b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.34ex; height:2.843ex;" alt="{\displaystyle \ (a_{n})_{n\in \mathbb {N} }}"></span> שמקיימות <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 _{n=1}^{\infty }|a_{n}|<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \sum _{n=1}^{\infty }|a_{n}|<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cac02dc467e7a64ca8e349d91be7747f9ef425fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:13.874ex; height:6.843ex;" alt="{\displaystyle \ \sum _{n=1}^{\infty }|a_{n}|<\infty }"></span> הוא מרחב בנך עם הנורמה <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 \|(a_{n})\|_{1}=\sum _{n=1}^{\infty }|a_{n}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|(a_{n})\|_{1}=\sum _{n=1}^{\infty }|a_{n}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d135c138ab9bfaa2c37e15b08d4203afcc661410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.219ex; height:6.843ex;" alt="{\displaystyle \|(a_{n})\|_{1}=\sum _{n=1}^{\infty }|a_{n}|}"></span>. מרחב זה מסומן 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 \ \ell _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \ell _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/741f73cf76ae3ed2ad278e034a26637096867617" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \ \ell _{1}}"></span>.</li></ul> <ul><li>כהכללה של הדוגמה הקודמת, 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 \ 1\leq p<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mn>1</mn> <mo>≤</mo> <mi>p</mi> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ 1\leq p<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8c476df1d6f19d03c91c9d0b56ccbf08ee04c918" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.433ex; height:2.509ex;" alt="{\displaystyle \ 1\leq p<\infty }"></span>, מגדירים את 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 \ \ell _{p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \ell _{p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21ee0dfdaf945428e59d1dcbaf47c8a557e92a46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.609ex; height:2.843ex;" alt="{\displaystyle \ \ell _{p}}"></span> להיות אוסף הסדרות <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 \ (a_{n})_{n\in \mathbb {N} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <msub> <mi>a</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> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (a_{n})_{n\in \mathbb {N} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbef5de6febc60de99017922f0f44fdd83d516b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.34ex; height:2.843ex;" alt="{\displaystyle \ (a_{n})_{n\in \mathbb {N} }}"></span> שמקיימות <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 _{n=1}^{\infty }|a_{n}|^{p}<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \sum _{n=1}^{\infty }|a_{n}|^{p}<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f938305091e520f6c16284e19893a05bb92db36f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.933ex; height:6.843ex;" alt="{\displaystyle \ \sum _{n=1}^{\infty }|a_{n}|^{p}<\infty }"></span>. מרחב זה הוא מרחב בנך תחת הנורמה <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 \|(a_{n})\|_{p}=\left(\sum _{n=1}^{\infty }|a_{n}|^{p}\right)^{1/p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">‖</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>p</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \|(a_{n})\|_{p}=\left(\sum _{n=1}^{\infty }|a_{n}|^{p}\right)^{1/p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/03afc4c3efa50d371a8cf1a9fcab7407c40c1c17" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:25.668ex; height:8.009ex;" alt="{\displaystyle \|(a_{n})\|_{p}=\left(\sum _{n=1}^{\infty }|a_{n}|^{p}\right)^{1/p}}"></span>. 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 \ p=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>p</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cde30e4689aae23448071197f8f0bc03be71264" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.172ex; height:2.009ex;" alt="{\displaystyle \ p=\infty }"></span> מגדירים את 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 \ \ell _{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \ell _{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/164c2e06307caca10d5fcb2162db5ee2c37e994d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.426ex; height:2.509ex;" alt="{\displaystyle \ \ell _{\infty }}"></span> להיות אוסף הסדרות החסומות עם הנורמה <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 \ \|(a_{n})\|_{\infty }=\sup |a_{n}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo fence="false" stretchy="false">‖</mo> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <msub> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msub> <mo>=</mo> <mo movablelimits="true" form="prefix">sup</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \|(a_{n})\|_{\infty }=\sup |a_{n}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb2d997bbfb8e1eb859c184b4f49f2313e7e7feb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.767ex; height:2.843ex;" alt="{\displaystyle \ \|(a_{n})\|_{\infty }=\sup |a_{n}|}"></span> וזהו מרחב נורמי. 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 \ p<1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>p</mi> <mo><</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p<1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c074f79d64c8995c4ae3f586b70487ae5e0252af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.011ex; height:2.509ex;" alt="{\displaystyle \ p<1}"></span>, המרחב המתקבל הוא מרחב מטרי שלם (ואפילו <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>) אבל איננו מרחב בנך כי אין עליו נורמה.</li></ul> <div class="mw-heading mw-heading3"><h3 id="מרחבי_פונקציות"><span id=".D7.9E.D7.A8.D7.97.D7.91.D7.99_.D7.A4.D7.95.D7.A0.D7.A7.D7.A6.D7.99.D7.95.D7.AA"></span>מרחבי פונקציות</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%91%D7%A0%D7%9A&action=edit&section=4" title="עריכת קוד המקור של הפרק: מרחבי פונקציות"><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%91%D7%A0%D7%9A&veaction=edit&section=4" title="עריכת פסקה: "מרחבי פונקציות"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>אוסף רחב יותר של דוגמאות מתקבל באופן הבא: 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 \ (X,\mu )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ (X,\mu )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ab1c3773f29f2dee6f64ed1c8d8d826c4fbb4b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.806ex; height:2.843ex;" alt="{\displaystyle \ (X,\mu )}"></span> הוא <a href="/wiki/%D7%9E%D7%99%D7%93%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="מידה (מתמטיקה)">מרחב מידה</a> מגדירים את <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}(X,\mu )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ L_{p}(X,\mu )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/681c7bb6cb459a3c28ef4cc2d3681b0a0fbfde62" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.448ex; height:3.009ex;" alt="{\displaystyle \ L_{p}(X,\mu )}"></span> להיות אוסף מחלקות השקילות של 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:X\to \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <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/fa21e54761bacd9c08bb8381698df2a7a978d715" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.069ex; height:2.509ex;" alt="{\displaystyle \ f:X\to \mathbb {C} }"></span> המקיימות <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(x)|^{p}d\mu (x)<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>d</mi> <mi>μ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \int _{X}|f(x)|^{p}d\mu (x)<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e4ccc3dd4f346b127f195902761422cae57e001" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:22.229ex; height:5.676ex;" alt="{\displaystyle \ \int _{X}|f(x)|^{p}d\mu (x)<\infty }"></span> תחת <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> של שוויון כמעט תמיד. מרחב זה הוא מרחב בנך תחת הנורמה</li></ul> <p><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\|_{p}=\left(\int _{X}|f(x)|^{p}d\mu (x)\right)^{1/p}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo fence="false" stretchy="false">‖</mo> <mi>f</mi> <msub> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mo>∫</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msup> <mi>d</mi> <mi>μ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>p</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \|f\|_{p}=\left(\int _{X}|f(x)|^{p}d\mu (x)\right)^{1/p}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb8e37c8e32c8193f6f6c2984b68e55fd507f1b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.305ex; height:6.676ex;" alt="{\displaystyle \ \|f\|_{p}=\left(\int _{X}|f(x)|^{p}d\mu (x)\right)^{1/p}}"></span> </p> <ul><li><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%A1%D7%95%D7%9E%D7%95%D7%AA&action=edit&redlink=1" class="new" title="מרחב הפונקציות החסומות (הדף אינו קיים)">מרחב הפונקציות החסומות</a> ממשיך את הדוגמה הקודמת למקרה <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=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>p</mi> <mo>=</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0cde30e4689aae23448071197f8f0bc03be71264" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.172ex; height:2.009ex;" alt="{\displaystyle \ p=\infty }"></span>. אם X <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99" title="מרחב מטרי">מרחב מטרי</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 \ L^{\infty }(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </msup> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ L^{\infty }(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be9f8e2896e98f2ec350dc3d6a6b4378d13abb5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.828ex; height:2.843ex;" alt="{\displaystyle \ L^{\infty }(X)}"></span> הוא המרחב של ה<a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%97%D7%A1%D7%95%D7%9E%D7%94" title="פונקציה חסומה">פונקציות החסומות</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 \ X\rightarrow \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <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 \ X\rightarrow \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0849a50c32f38d4310c4e7e68d4bf4a4bfbae86b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.853ex; height:2.176ex;" alt="{\displaystyle \ X\rightarrow \mathbb {C} }"></span> (לפעמים מדובר ב<a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%9E%D7%9E%D7%A9%D7%99%D7%AA" title="פונקציה ממשית">פונקציות ממשיות</a> דווקא). זהו <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>, עם נורמת הסופרימום של הפונקציות. <b>שיכון קורטובסקי</b> (<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\mapsto (y\mapsto d(x,y)-d(x_{0},y))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>x</mi> <mo stretchy="false">↦</mo> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">↦</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>−</mo> <mi>d</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ x\mapsto (y\mapsto d(x,y)-d(x_{0},y))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3b10b16378fc75abe4546ff1db63999cfabc5e50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.086ex; height:2.843ex;" alt="{\displaystyle \ x\mapsto (y\mapsto d(x,y)-d(x_{0},y))}"></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_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,x_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/863f8f233de85b1564c1c8fc41926518192eddc2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.771ex; height:2.009ex;" alt="{\displaystyle \,x_{0}}"></span> נקודה קבועה) מראה שכל מרחב מטרי משוכן במרחב הפונקציות החסומות המתאים לו.</li></ul> <ul><li><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)">מרחב הפונקציות הרציפות</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 \ C(X)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>C</mi> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ C(X)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7182c818878e500ca1855f20f75ebb08ec6cbe7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.136ex; height:2.843ex;" alt="{\displaystyle \ C(X)}"></span> מ<a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99" title="מרחב מטרי">מרחב מטרי</a> X אל המספרים המרוכבים (או הממשיים).</li></ul> <div class="mw-heading mw-heading2"><h2 id="טיפוסים_של_מרחבי_בנך"><span id=".D7.98.D7.99.D7.A4.D7.95.D7.A1.D7.99.D7.9D_.D7.A9.D7.9C_.D7.9E.D7.A8.D7.97.D7.91.D7.99_.D7.91.D7.A0.D7.9A"></span>טיפוסים של מרחבי בנך</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%91%D7%A0%D7%9A&action=edit&section=5" title="עריכת קוד המקור של הפרק: טיפוסים של מרחבי בנך"><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%91%D7%A0%D7%9A&veaction=edit&section=5" title="עריכת פסקה: "טיפוסים של מרחבי בנך"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">מרחבי הילברט</a> הם דוגמה קיצונית של מרחבי בנך, ותכונות שונות של מרחבי בנך מודדות עד כמה הם קרובים להיות מרחבי הילברט. </p><p>מרחב ה<a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C" title="פונקציונל">פונקציונלים</a> הליניארים על מרחב בנך <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"> <mtext> </mtext> <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/a96dd62d4cca19aa212ae1216891f4388ca4be24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.561ex; height:2.176ex;" alt="{\displaystyle \ X}"></span> גם הוא מרחב בנך תחת הנורמה <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 \ \|\varphi \|=\sup _{x\in X,\|x\|=1}\varphi (x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mo fence="false" stretchy="false">‖</mo> <mi>φ</mi> <mo fence="false" stretchy="false">‖</mo> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">sup</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo>∈</mo> <mi>X</mi> <mo>,</mo> <mo fence="false" stretchy="false">‖</mo> <mi>x</mi> <mo fence="false" stretchy="false">‖</mo> <mo>=</mo> <mn>1</mn> </mrow> </munder> <mi>φ</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \|\varphi \|=\sup _{x\in X,\|x\|=1}\varphi (x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2e552cd51e8f31167fa0a42e630d149c1c76842e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:21.149ex; height:5.009ex;" alt="{\displaystyle \ \|\varphi \|=\sup _{x\in X,\|x\|=1}\varphi (x)}"></span> מרחב זה מסומן לרוב 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 \ X^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </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/65bbd1bc6c404017d42d7f9c937a09075d0dab8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.632ex; height:2.343ex;" alt="{\displaystyle \ X^{*}}"></span>. לדוגמה, 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 \ {\frac {1}{p}}+{\frac {1}{q}}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>p</mi> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>q</mi> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ {\frac {1}{p}}+{\frac {1}{q}}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e086bd68e62396404bd43f6e3b6edfc3d5eb1b44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.686ex; height:5.676ex;" alt="{\displaystyle \ {\frac {1}{p}}+{\frac {1}{q}}=1}"></span> וגם <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<\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <mi>p</mi> <mo><</mo> <mi mathvariant="normal">∞</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ p<\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7962774512290747c169ab5c774b3d7dae554960" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.172ex; height:2.176ex;" alt="{\displaystyle \ p<\infty }"></span> אז <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 _{p}^{*}=\ell _{q}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>=</mo> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{p}^{*}=\ell _{q}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/33e6b29dd3404134bbf5ab131525ce19842b50bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.086ex; height:2.843ex;" alt="{\displaystyle \ell _{p}^{*}=\ell _{q}}"></span>. לעומת זאת, <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 _{\infty }^{*}\neq \ell _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msubsup> <mo>≠</mo> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ell _{\infty }^{*}\neq \ell _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/97beebc17dc51d29ab02a6a2c301d5250b8d11e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.967ex; height:2.676ex;" alt="{\displaystyle \ell _{\infty }^{*}\neq \ell _{1}}"></span>. מדוגמה זו רואים שלא תמיד מתקיים <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^{**}=X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> <mo>∗</mo> </mrow> </msup> <mo>=</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,X^{**}=X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca3c7f4e7ab378a0af90f0c2501634e30f0d5b5b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:9.339ex; height:2.343ex;" alt="{\displaystyle \,X^{**}=X}"></span>. לעומת זאת, יש שיכון טבעי <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\hookrightarrow X^{**}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>X</mi> <mo stretchy="false">↪</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,X\hookrightarrow X^{**}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b3a036b3c64de36398a872abc57d32b6179a027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.147ex; height:2.343ex;" alt="{\displaystyle \,X\hookrightarrow X^{**}}"></span>. מרחב בנך שעבורו השיכון <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\hookrightarrow X^{**}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mi>X</mi> <mo stretchy="false">↪</mo> <msup> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,X\hookrightarrow X^{**}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b3a036b3c64de36398a872abc57d32b6179a027" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:10.147ex; height:2.343ex;" alt="{\displaystyle \,X\hookrightarrow X^{**}}"></span> 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">איזומורפיזם</a> נקרא <b>מרחב רפלקסיבי</b>. כל מרחב הילברט הוא רפלקסיבי. </p><p>מרחב בנך שלכל תת-מרחב ספרבילי שלו, A, גם <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 \ A^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ A^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/05f1ceaca04ab0acaec418f52da844baca398a92" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.378ex; height:2.343ex;" alt="{\displaystyle \ A^{*}}"></span> הוא ספרבילי, נקרא <b>מרחב Asplund</b>; כל מרחב רפלקסיבי הוא Asplund. </p><p>מרחב בנך שאינו מכיל עותק איזומורפי 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 \ \ell _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mtext> </mtext> <msub> <mi>ℓ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ \ell _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/741f73cf76ae3ed2ad278e034a26637096867617" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \ \ell _{1}}"></span> נקרא <b>מרחב Rosenthal</b>. כל מרחב Asplund הוא Rosenthal. </p><p>כל מרחב בנך רפלקסיבי הוא <b>נוצר קומפקטית-חלש</b> (weakly compactly generated), כלומר, יש בו <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">קבוצה קומפקטית</a> (בטופולוגיה החלשה), הפורשת מרחב צפוף. כל מרחב כזה הוא <b>Weakly Lindelof determined</b> (יש בו קבוצה M הפורשת מרחב צפוף, כך שהחיתוך שלה עם התומך של כל פונקציונל ליניארי הוא בן-מניה). מרחב מסוג זה, שהוא Asplund, הוא ספרבילי. </p> <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%91%D7%A0%D7%9A&action=edit&section=6" 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%91%D7%A0%D7%9A&veaction=edit&section=6" 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%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 (אנליזה)</a></li> <li><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99" title="מרחב מטרי">מרחב מטרי</a></li> <li><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></li> <li><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">מרחב הילברט</a></li> <li><a href="/wiki/%D7%90%D7%95%D7%A4%D7%A8%D7%98%D7%95%D7%A8" title="אופרטור">אופרטור</a></li> <li><a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%95%D7%A0%D7%9C" title="פונקציונל">פונקציונל</a></li> <li><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%90%D7%9F-%D7%91%D7%A0%D7%9A" title="משפט האן-בנך">משפט האן-בנך</a></li> <li><a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%91%D7%A0%D7%9A-%D7%A9%D7%98%D7%99%D7%99%D7%A0%D7%94%D7%90%D7%95%D7%A1" title="משפט בנך-שטיינהאוס">משפט בנך-שטיינהאוס</a></li> <li><a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94" title="טופולוגיה">טופולוגיה</a></li> <li><a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%AA" title="אנליזה מתמטית">אנליזה מתמטית</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></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%91%D7%A0%D7%9A&action=edit&section=7" 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%91%D7%A0%D7%9A&veaction=edit&section=7" 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:Banach_spaces" class="extiw" title="commons:Category:Banach spaces">מרחב בנך</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.encyclopediaofmath.org/index.php/Banach_space">מרחב בנך</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%9C%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="אנציקלופדיה למתמטיקה">אנציקלופדיה למתמטיקה</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/BanachSpace.html">מרחב בנך</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/987007282589705171">מרחבי בנך</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> <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 class="mw-selflink selflink">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 class="mw-selflink selflink">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 href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">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 href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">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 class="mw-selflink selflink">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 class="mw-selflink selflink">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 href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">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 href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%99%D7%9C%D7%91%D7%A8%D7%98" title="מרחב הילברט">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/Q194397?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/Q194397?uselang=he&#124;עריכת_הנתון_בוויקינתונים" scope="row" 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