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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%A1%D7%92%D7%95%D7%A8+%28%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94%29" title="מומלץ ליצור חשבון ולהיכנס אליו, אך אין חובה לעשות זאת" class=""><span>יצירת חשבון</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%9B%D7%A0%D7%99%D7%A1%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%A1%D7%92%D7%95%D7%A8+%28%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94%29" title="מומלץ להיכנס לחשבון, אך אין חובה לעשות זאת [o]" accesskey="o" class=""><span>כניסה לחשבון</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="אפשרויות נוספות" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="כלים אישיים" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">כלים אישיים</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="תפריט משתמש" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_he.wikipedia.org&uselang=he"><span>תרומה לוויקיפדיה</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D7%9E%D7%99%D7%95%D7%97%D7%93:%D7%94%D7%A8%D7%A9%D7%9E%D7%94_%D7%9C%D7%97%D7%A9%D7%91%D7%95%D7%9F&returnto=%D7%A1%D7%92%D7%95%D7%A8+%28%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94%29" 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%A1%D7%92%D7%95%D7%A8+%28%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94%29" 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]" 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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-הגדרה_פורמלית" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#הגדרה_פורמלית"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>הגדרה פורמלית</span> </div> </a> <ul id="toc-הגדרה_פורמלית-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> <ul id="toc-דוגמאות-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-תכונות_הנוגעות_לסגור" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#תכונות_הנוגעות_לסגור"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>תכונות הנוגעות לסגור</span> </div> </a> <ul id="toc-תכונות_הנוגעות_לסגור-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">4</span> <span>קישורים חיצוניים</span> </div> </a> <ul id="toc-קישורים_חיצוניים-sublist" class="vector-toc-list"> </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">סגור (טופולוגיה)</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־23 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-23" 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">23 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/Closure_(topology)" title="Closure (topology) – אנגלית" lang="en" hreflang="en" data-title="Closure (topology)" 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/%D8%BA%D8%A7%D9%84%D9%82_(%D8%B7%D9%88%D8%A8%D9%88%D9%84%D9%88%D8%AC%D9%8A%D8%A7)" title="غالق (طوبولوجيا) – ערבית" lang="ar" hreflang="ar" data-title="غالق (طوبولوجيا)" data-language-autonym="العربية" data-language-local-name="ערבית" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Clausura_topol%C3%B2gica" title="Clausura topològica – קטלאנית" lang="ca" hreflang="ca" data-title="Clausura topològica" data-language-autonym="Català" data-language-local-name="קטלאנית" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Uz%C3%A1v%C4%9Br_mno%C5%BEiny" title="Uzávěr množiny – צ׳כית" lang="cs" hreflang="cs" data-title="Uzávěr množiny" 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/Abgeschlossene_H%C3%BClle" title="Abgeschlossene Hülle – גרמנית" lang="de" hreflang="de" data-title="Abgeschlossene Hülle" data-language-autonym="Deutsch" data-language-local-name="גרמנית" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Ferma%C4%B5o" title="Fermaĵo – אספרנטו" lang="eo" hreflang="eo" data-title="Fermaĵo" 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/Clausura_topol%C3%B3gica" title="Clausura topológica – ספרדית" lang="es" hreflang="es" data-title="Clausura topológica" 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/Sulund_(topoloogia)" title="Sulund (topoloogia) – אסטונית" lang="et" hreflang="et" data-title="Sulund (topoloogia)" data-language-autonym="Eesti" data-language-local-name="אסטונית" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Itxitura_(topologia)" title="Itxitura (topologia) – בסקית" lang="eu" hreflang="eu" data-title="Itxitura (topologia)" data-language-autonym="Euskara" data-language-local-name="בסקית" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Topologinen_sulkeuma" title="Topologinen sulkeuma – פינית" lang="fi" hreflang="fi" data-title="Topologinen sulkeuma" 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/Adh%C3%A9rence_(math%C3%A9matiques)" title="Adhérence (mathématiques) – צרפתית" lang="fr" hreflang="fr" data-title="Adhérence (mathématiques)" 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/Halmaz_lez%C3%A1rtja" title="Halmaz lezártja – הונגרית" lang="hu" hreflang="hu" data-title="Halmaz lezártja" data-language-autonym="Magyar" data-language-local-name="הונגרית" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Chiusura_(topologia)" title="Chiusura (topologia) – איטלקית" lang="it" hreflang="it" data-title="Chiusura (topologia)" 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/%E9%96%89%E5%8C%85_(%E4%BD%8D%E7%9B%B8%E7%A9%BA%E9%96%93%E8%AB%96)" title="閉包 (位相空間論) – יפנית" lang="ja" hreflang="ja" data-title="閉包 (位相空間論)" data-language-autonym="日本語" data-language-local-name="יפנית" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8F%90%ED%8F%AC_(%EC%9C%84%EC%83%81%EC%88%98%ED%95%99)" title="폐포 (위상수학) – קוריאנית" lang="ko" hreflang="ko" data-title="폐포 (위상수학)" 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/Afsluiting_(topologie)" title="Afsluiting (topologie) – הולנדית" lang="nl" hreflang="nl" data-title="Afsluiting (topologie)" 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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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> השייכת ל<a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב טופולוגי">מרחב טופולוגי</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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> הוא <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A1%D7%92%D7%95%D7%A8%D7%94" title="קבוצה סגורה">הקבוצה הסגורה</a> הקטנה ביותר ה<a href="/wiki/%D7%AA%D7%AA-%D7%A7%D7%91%D7%95%D7%A6%D7%94" title="תת-קבוצה">מכילה</a> 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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. מבחינה אינטואיטיבית אפשר לחשוב עליו כעל קבוצה המכילה את <a href="/wiki/%D7%90%D7%99%D7%91%D7%A8_(%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%95%D7%AA)" title="איבר (תורת הקבוצות)">אברי</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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> ואת כל הנקודות ש"נוגעות" בקבוצה <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="הגדרה_פורמלית"><span id=".D7.94.D7.92.D7.93.D7.A8.D7.94_.D7.A4.D7.95.D7.A8.D7.9E.D7.9C.D7.99.D7.AA"></span>הגדרה פורמלית</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&action=edit&section=1" title="עריכת קוד המקור של הפרק: הגדרה פורמלית"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&veaction=edit&section=1" title="עריכת פסקה: "הגדרה פורמלית"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>יהא <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"> <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> מרחב טופולוגי כלשהו, ותהא <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\subseteq X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>⊆</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\subseteq X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44aba72977e43f863dd873b095d1dc0bd3f17608" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.578ex; height:2.343ex;" alt="{\displaystyle S\subseteq X}"></span> קבוצה. 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 \Lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ac0a4a98a414e3480335f9ba652d12571ec6733" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.613ex; height:2.176ex;" alt="{\displaystyle \Lambda }"></span> היא קבוצת הקבוצות הסגורות <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"> <mi>A</mi> </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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></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 S\subseteq A\subseteq X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>⊆</mo> <mi>A</mi> <mo>⊆</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S\subseteq A\subseteq X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/621eeec91d593141734c66ba8f79f573c2f70432" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:11.419ex; height:2.343ex;" alt="{\displaystyle S\subseteq A\subseteq X}"></span> (כלומר, קבוצת הקבוצות הסגורות המכילות 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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>), אז ה<b>סגור</b> 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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> יסומן <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(S)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(S)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef26ed096a5a43450d992243281fc50ed7fab873" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.633ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}(S)}"></span> או <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 {\overline {S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0353b71f671221a0796d94febf9079b11dcca124" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.663ex; height:3.009ex;" alt="{\displaystyle {\overline {S}}}"></span>, ויוגדר על ידי: </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {S}}={\mbox{Cl}}(S)=\bigcap _{A\in \Lambda }A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>S</mi> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>⋂</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> <mo>∈</mo> <mi mathvariant="normal">Λ</mi> </mrow> </munder> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\overline {S}}={\mbox{Cl}}(S)=\bigcap _{A\in \Lambda }A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ee9497576df9d1bfcf3d6a01e076b7bd98c479fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:19.093ex; height:5.843ex;" alt="{\displaystyle {\overline {S}}={\mbox{Cl}}(S)=\bigcap _{A\in \Lambda }A}"></span>.</dd></dl></dd></dl> <p>להלן מספר הגדרות אלטרנטיביות ששקולות להגדרה לעיל (כלומר, ניתן להוכיח אותן מההגדרה, ואם מקבלים אותן כהגדרה, ניתן להוכיח מהן את ההגדרה המקורית): </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(S)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(S)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef26ed096a5a43450d992243281fc50ed7fab873" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.633ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}(S)}"></span> היא קבוצת כל האיברים 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 X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> שבכל <a href="/wiki/%D7%A1%D7%91%D7%99%D7%91%D7%94_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" class="mw-redirect" title="סביבה (טופולוגיה)">סביבה</a> שלהם קיים איבר 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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span> (לא בהכרח שונה מהם).</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(S)=S\cup S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>S</mi> <mo>∪</mo> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(S)=S\cup S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f68fc23142e7221ef33e7980d121eaf1f76cd967" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.02ex; height:3.009ex;" alt="{\displaystyle {\mbox{Cl}}(S)=S\cup S'}"></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 S'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>S</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf9961844d1f539adee019e432dc18aa2a7ede59" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.206ex; height:2.509ex;" alt="{\displaystyle S'}"></span> היא <a href="/wiki/%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%94%D7%A0%D7%92%D7%96%D7%A8%D7%AA" title="הקבוצה הנגזרת">הקבוצה הנגזרת</a> 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 S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4611d85173cd3b508e67077d4a1252c9c05abca2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle S}"></span>.</li> <li>הגדרה באמצעות ה<a href="/wiki/%D7%A4%D7%A0%D7%99%D7%9D_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="פנים (טופולוגיה)">פנים</a> של ה<a href="/wiki/%D7%9E%D7%A9%D7%9C%D7%99%D7%9D_(%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%A7%D7%91%D7%95%D7%A6%D7%95%D7%AA)" class="mw-redirect" title="משלים (תורת הקבוצות)">משלים</a> של הקבוצה: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(A)=\left({\mbox{Int}}(A^{C})\right)^{C}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Int</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>C</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(A)=\left({\mbox{Int}}(A^{C})\right)^{C}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/098b0764ed519c2cf9eaa5ff291e07204b0ce1b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:20.657ex; height:3.843ex;" alt="{\displaystyle {\mbox{Cl}}(A)=\left({\mbox{Int}}(A^{C})\right)^{C}}"></span>.</li></ul> <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%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&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%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&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>הסגור של <a href="/wiki/%D7%A7%D7%98%D7%A2_%D7%A4%D7%AA%D7%95%D7%97" class="mw-redirect" title="קטע פתוח">הקטע הפתוח</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 (a,b)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d7e5710198f33b00695903460983021e75860e2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.071ex; height:2.843ex;" alt="{\displaystyle (a,b)}"></span> הוא הקטע הסגור <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,b]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [a,b]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c4b788fc5c637e26ee98b45f89a5c08c85f7935" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.555ex; height:2.843ex;" alt="{\displaystyle [a,b]}"></span>.</li> <li>הסגור של <a href="/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%A8%D7%A6%D7%99%D7%95%D7%A0%D7%9C%D7%99" title="מספר רציונלי">קבוצת המספרים הרציונלים</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 \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }"></span> הוא <a href="/wiki/%D7%94%D7%99%D7%A9%D7%A8_%D7%94%D7%9E%D7%9E%D7%A9%D7%99" title="הישר הממשי">הישר הממשי</a> כולו <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>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="תכונות_הנוגעות_לסגור"><span id=".D7.AA.D7.9B.D7.95.D7.A0.D7.95.D7.AA_.D7.94.D7.A0.D7.95.D7.92.D7.A2.D7.95.D7.AA_.D7.9C.D7.A1.D7.92.D7.95.D7.A8"></span>תכונות הנוגעות לסגור</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D7%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&action=edit&section=3" title="עריכת קוד המקור של הפרק: תכונות הנוגעות לסגור"><span>עריכת קוד מקור</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D7%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&veaction=edit&section=3" title="עריכת פסקה: "תכונות הנוגעות לסגור"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>כל קבוצה סגורה שווה לסגור של עצמה: <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={\mbox{Cl}}(A)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A={\mbox{Cl}}(A)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3bd639feeab3f31ffc2b637ae34a1b105134ce1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.719ex; height:2.843ex;" alt="{\displaystyle A={\mbox{Cl}}(A)}"></span>. בפרט הסגור הוא קבוצה סגורה ולכן <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(A)={\mbox{Cl}}\left({\mbox{Cl}}(A)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(A)={\mbox{Cl}}\left({\mbox{Cl}}(A)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d73478309b695c7ac2abec5aa6be54447e862c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.374ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}(A)={\mbox{Cl}}\left({\mbox{Cl}}(A)\right)}"></span>.</li> <li><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\subseteq B\Rightarrow {\mbox{Cl}}(A)\subseteq {\mbox{Cl}}(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>⊆</mo> <mi>B</mi> <mo stretchy="false">⇒</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\subseteq B\Rightarrow {\mbox{Cl}}(A)\subseteq {\mbox{Cl}}(B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7c886567649a4735360fbfda8622b9a2a6fc677" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.094ex; height:2.843ex;" alt="{\displaystyle A\subseteq B\Rightarrow {\mbox{Cl}}(A)\subseteq {\mbox{Cl}}(B)}"></span>.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}\left(A\cap B\right)\subseteq {\mbox{Cl}}(A)\cap {\mbox{Cl}}(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mo>∩</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>∩</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}\left(A\cap B\right)\subseteq {\mbox{Cl}}(A)\cap {\mbox{Cl}}(B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c873485535f8f86199302ce2350cd2c8dca26ed3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.068ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}\left(A\cap B\right)\subseteq {\mbox{Cl}}(A)\cap {\mbox{Cl}}(B)}"></span>.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}\left(A\cup B\right)={\mbox{Cl}}(A)\cup {\mbox{Cl}}(B)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <mi>A</mi> <mo>∪</mo> <mi>B</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>∪</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>B</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}\left(A\cup B\right)={\mbox{Cl}}(A)\cup {\mbox{Cl}}(B)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3afcaedbf06ee6ce8e7a0e07a33db6358d70e284" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.068ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}\left(A\cup B\right)={\mbox{Cl}}(A)\cup {\mbox{Cl}}(B)}"></span>.</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> היא <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%A8%D7%A6%D7%99%D7%A4%D7%94_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="פונקציה רציפה (טופולוגיה)">פונקציה רציפה</a> אם ורק אם לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> ב<a href="/wiki/%D7%AA%D7%97%D7%95%D7%9D_%D7%A9%D7%9C_%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94" title="תחום של פונקציה">תחום</a> שלה 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 f\left({\mbox{Cl}}(A)\right)\subseteq {\mbox{Cl}}\left(f(A)\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f\left({\mbox{Cl}}(A)\right)\subseteq {\mbox{Cl}}\left(f(A)\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d88dc65a9d97fa9a8b0324c71d4fcbee44dffe2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.803ex; height:2.843ex;" alt="{\displaystyle f\left({\mbox{Cl}}(A)\right)\subseteq {\mbox{Cl}}\left(f(A)\right)}"></span>.</li> <li>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 A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> <a href="/wiki/%D7%A7%D7%A9%D7%99%D7%A8%D7%95%D7%AA_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" class="mw-redirect" title="קשירות (טופולוגיה)">קבוצה קשירה</a>, לכל <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\subseteq B\subseteq {\mbox{Cl}}(A)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>⊆</mo> <mi>B</mi> <mo>⊆</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A\subseteq B\subseteq {\mbox{Cl}}(A)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff65e19fd071789b2437d917fab1247e0a2d852c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.581ex; height:2.843ex;" alt="{\displaystyle A\subseteq B\subseteq {\mbox{Cl}}(A)}"></span> מתקיים שגם <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 B}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>B</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle B}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47136aad860d145f75f3eed3022df827cee94d7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle B}"></span> קבוצה קשירה. בפרט, הסגור של קבוצה קשירה גם הוא קשיר.</li> <li>קבוצה <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"> <mi>A</mi> </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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> במרחב <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"> <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> המקיימת <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Cl}}(A)=X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Cl}}(A)=X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58d7b475bbda0d0e80d18dc821097a2a682cf3e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.956ex; height:2.843ex;" alt="{\displaystyle {\mbox{Cl}}(A)=X}"></span> נקראת <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A6%D7%A4%D7%95%D7%A4%D7%94" title="קבוצה צפופה">קבוצה צפופה</a>.</li> <li>קבוצה <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"> <mi>A</mi> </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/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> במרחב <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"> <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/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> המקיימת <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{Int}}\left({\mbox{Cl}}(A)\right)=\emptyset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Int</mtext> </mstyle> </mrow> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>Cl</mtext> </mstyle> </mrow> <mo stretchy="false">(</mo> <mi>A</mi> <mo stretchy="false">)</mo> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi mathvariant="normal">∅</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{Int}}\left({\mbox{Cl}}(A)\right)=\emptyset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44fcb583be226ee35729e154f245213c81f8afc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.371ex; height:2.843ex;" alt="{\displaystyle {\mbox{Int}}\left({\mbox{Cl}}(A)\right)=\emptyset }"></span> נקראת <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%93%D7%9C%D7%99%D7%9C%D7%94" title="קבוצה דלילה">קבוצה דלילה</a>.</li></ul> <p>נשים לב שרבות מתכונות אלו מזכירות את תכונות ה<a href="/wiki/%D7%A4%D7%A0%D7%99%D7%9D_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="פנים (טופולוגיה)">פנים</a>. </p> <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%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&action=edit&section=4" 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%A1%D7%92%D7%95%D7%A8_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)&veaction=edit&section=4" title="עריכת פסקה: "קישורים חיצוניים"" class="mw-editsection-visualeditor"><span>עריכה</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/TopologicalClosure.html">סגור</a>, באתר <a href="/wiki/MathWorld" title="MathWorld">MathWorld</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></ul> <p><br /> </p> <table class="navbox nowraplinks mw-collapsible mw-collapsed" style="width: 90%; clear: both; margin: 0.5em auto; margin-top: 0.5em; margin-bottom: 0.5em; padding: 0.2em; text-align: right;"> <tbody><tr> <th colspan="3" style="text-align: center; padding-top: 0.1em; padding-bottom: 0.1em; color: black; background:#d1eeee; font-weight: bold;"><a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%A7%D7%91%D7%95%D7%A6%D7%AA%D7%99%D7%AA" title="טופולוגיה קבוצתית">טופולוגיה קבוצתית</a> </th></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">מושגי יסוד </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%98%D7%A8%D7%99" title="מרחב מטרי">מרחב מטרי</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99" title="מרחב טופולוגי">מרחב טופולוגי</a> • <a href="/wiki/%D7%A4%D7%95%D7%A0%D7%A7%D7%A6%D7%99%D7%94_%D7%A8%D7%A6%D7%99%D7%A4%D7%94_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="פונקציה רציפה (טופולוגיה)">פונקציה רציפה</a> • <a href="/wiki/%D7%94%D7%95%D7%9E%D7%99%D7%90%D7%95%D7%9E%D7%95%D7%A8%D7%A4%D7%99%D7%96%D7%9D" title="הומיאומורפיזם">הומיאומורפיזם</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">בתוך המרחב </td> <td style="padding-right: 5px; text-align: right;"><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">קבוצה פתוחה</a> • <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A1%D7%92%D7%95%D7%A8%D7%94" title="קבוצה סגורה">קבוצה סגורה</a> • <a href="/wiki/%D7%A4%D7%A0%D7%99%D7%9D_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="פנים (טופולוגיה)">פנים</a> • <a class="mw-selflink selflink">סגור</a> • <a href="/wiki/%D7%A9%D7%A4%D7%94_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" title="שפה (טופולוגיה)">שפה</a> • <a href="/wiki/%D7%A1%D7%91%D7%99%D7%91%D7%94_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" class="mw-redirect" title="סביבה (טופולוגיה)">סביבה</a> • <a href="/wiki/%D7%A0%D7%A7%D7%95%D7%93%D7%AA_%D7%94%D7%A6%D7%98%D7%91%D7%A8%D7%95%D7%AA" title="נקודת הצטברות">נקודת הצטברות</a> • <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%A6%D7%A4%D7%95%D7%A4%D7%94" title="קבוצה צפופה">קבוצה צפופה</a> • <a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%94_%D7%93%D7%9C%D7%99%D7%9C%D7%94" title="קבוצה דלילה">קבוצה דלילה</a> • <a href="/wiki/%D7%91%D7%A1%D7%99%D7%A1_%D7%9C%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94" class="mw-redirect" title="בסיס לטופולוגיה">בסיס</a> • <a href="/wiki/%D7%A1%D7%93%D7%A8%D7%AA_%D7%A7%D7%95%D7%A9%D7%99" title="סדרת קושי">סדרת קושי</a> </td></tr> <tr> <td colspan="2" style="background-color: #F2F3F4; text-align: center; font-weight: bold;">תכונות של מרחבים טופולוגיים </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%90%D7%A7%D7%A1%D7%99%D7%95%D7%9E%D7%95%D7%AA_%D7%94%D7%94%D7%A4%D7%A8%D7%93%D7%94" title="אקסיומות ההפרדה">אקסיומות ההפרדה</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_T0" class="mw-redirect" title="מרחב T0">T<sub>0</sub></a> • ‏ <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_T1" class="mw-redirect" title="מרחב T1">T<sub>1</sub></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">T<sub>2</sub></a> (מרחב האוסדורף) • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A8%D7%99%D7%A1%D7%95%D7%9F" class="mw-redirect" title="מרחב אוריסון">T<sub>2.5</sub></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_%D7%9C%D7%97%D7%9C%D7%95%D7%98%D7%99%D7%9F" class="mw-redirect" title="מרחב האוסדורף לחלוטין">מרחב האוסדורף לחלוטין</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A8%D7%92%D7%95%D7%9C%D7%A8%D7%99" title="מרחב רגולרי">T<sub>3</sub></a> (מרחב רגולרי) • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A8%D7%92%D7%95%D7%9C%D7%A8%D7%99_%D7%9C%D7%97%D7%9C%D7%95%D7%98%D7%99%D7%9F" title="מרחב רגולרי לחלוטין">T<sub>3.5</sub></a> • ‏ <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99" title="מרחב נורמלי">T<sub>4</sub></a> (מרחב נורמלי) • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99_%D7%9C%D7%97%D7%9C%D7%95%D7%98%D7%99%D7%9F" title="מרחב נורמלי לחלוטין">T<sub>5</sub></a> • ‏ <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A0%D7%95%D7%A8%D7%9E%D7%9C%D7%99_%D7%91%D7%90%D7%95%D7%A4%D7%9F_%D7%9E%D7%95%D7%A9%D7%9C%D7%9D" title="מרחב נורמלי באופן מושלם">T<sub>6</sub></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">מרחב מטריזבילי</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%90%D7%A7%D7%A1%D7%99%D7%95%D7%9E%D7%95%D7%AA_%D7%94%D7%9E%D7%A0%D7%99%D7%99%D7%94" title="אקסיומות המנייה">אקסיומות המנייה</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D0%A11" class="mw-redirect" title="מרחב С1">С<sub>1</sub></a> • ‏ <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D0%A12" class="mw-redirect" title="מרחב С2">С<sub>2</sub></a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A1%D7%A4%D7%A8%D7%91%D7%99%D7%9C%D7%99" title="מרחב ספרבילי">מרחב ספרבילי</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%95%D7%AA" class="mw-redirect" title="קומפקטיות">קומפקטיות</a> </td> <td style="padding-right: 5px; text-align: right;"><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> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA" title="מרחב קומפקטי מקומית">מרחב קומפקטי מקומית</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9C%D7%99%D7%A0%D7%93%D7%9C%D7%A3" title="מרחב לינדלף">מרחב לינדלף</a> • <a href="/w/index.php?title=%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_%D7%99%D7%97%D7%A1%D7%99%D7%AA&action=edit&redlink=1" class="new" title="קבוצה קומפקטית יחסית (הדף אינו קיים)">קבוצה קומפקטית יחסית</a> • <a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%A8%D7%94-%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99&action=edit&redlink=1" class="new" title="מרחב פרה-קומפקטי (הדף אינו קיים)">מרחב פרה-קומפקטי</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">תכונות נוספות </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%A9%D7%9C%D7%9D" class="mw-redirect" title="מרחב שלם">מרחב שלם</a> • <a href="/wiki/%D7%A7%D7%A9%D7%99%D7%A8%D7%95%D7%AA_(%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94)" class="mw-redirect" title="קשירות (טופולוגיה)">קשירות</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%91%D7%99%D7%99%D7%A8" class="mw-redirect" title="מרחב בייר">מרחב בייר</a> • <a href="/w/index.php?title=%D7%9E%D7%A8%D7%97%D7%91_%D7%A4%D7%95%D7%9C%D7%A0%D7%99&action=edit&redlink=1" class="new" title="מרחב פולני (הדף אינו קיים)">מרחב פולני</a> </td></tr> <tr> <td colspan="2" style="background-color: #F2F3F4; text-align: center; font-weight: bold;"><span style="color:#F2F3F4;"> ק </span> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">בניות </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%9B%D7%A4%D7%9C%D7%94" title="מרחב מכפלה">מרחב מכפלה</a> • <a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%9E%D7%95%D7%A9%D7%A8%D7%99%D7%AA" title="טופולוגיה מושרית">טופולוגיה מושרית</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9E%D7%A0%D7%94" title="מרחב מנה">מרחב מנה</a> • <p><a href="/wiki/%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%A4%D7%99%D7%A7%D7%A6%D7%99%D7%94" title="קומפקטיפיקציה">קומפקטיפיקציה</a> (<a href="/wiki/%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%A4%D7%99%D7%A7%D7%A6%D7%99%D7%94_%D7%97%D7%93-%D7%A0%D7%A7%D7%95%D7%93%D7%AA%D7%99%D7%AA" title="קומפקטיפיקציה חד-נקודתית">קומפקטיפיקציה חד-נקודתית</a>, <a href="/wiki/%D7%A7%D7%95%D7%9E%D7%A4%D7%A7%D7%98%D7%99%D7%A4%D7%99%D7%A7%D7%A6%D7%99%D7%99%D7%AA_%D7%A1%D7%98%D7%95%D7%9F-%D7%A6%27%D7%9A" title="קומפקטיפיקציית סטון-צ'ך">הקומפקטיפיקציה של סטון צ'ך</a>) • <a href="/wiki/%D7%94%D7%A9%D7%9C%D7%9E%D7%94_(%D7%9E%D7%A8%D7%97%D7%91%D7%99%D7%9D_%D7%9E%D7%98%D7%A8%D7%99%D7%99%D7%9D)" class="mw-redirect" title="השלמה (מרחבים מטריים)">השלמה</a> </p> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%9E%D7%A9%D7%A4%D7%98%D7%99%D7%9D_%D7%91%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94" title="קטגוריה:משפטים בטופולוגיה">משפטים</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%94%D7%9C%D7%9E%D7%94_%D7%A9%D7%9C_%D7%90%D7%95%D7%A8%D7%99%D7%A1%D7%95%D7%9F" title="הלמה של אוריסון">הלמה של אוריסון</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%98%D7%99%D7%98%D7%A6%D7%94" class="mw-redirect" title="משפט טיטצה">משפט טיטצה</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%9E%D7%98%D7%A8%D7%99%D7%96%D7%A6%D7%99%D7%94_%D7%A9%D7%9C_%D7%90%D7%95%D7%A8%D7%99%D7%A1%D7%95%D7%9F" class="mw-redirect" title="משפט המטריזציה של אוריסון">משפט המטריזציה של אוריסון</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%98%D7%99%D7%9B%D7%95%D7%A0%D7%95%D7%A3" title="משפט טיכונוף">משפט טיכונוף</a> • <a href="/wiki/%D7%9E%D7%A9%D7%A4%D7%98_%D7%94%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94_%D7%A9%D7%9C_%D7%91%D7%99%D7%99%D7%A8" class="mw-redirect" title="משפט הקטגוריה של בייר">משפט הקטגוריה של בייר</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;"><a href="/wiki/%D7%A7%D7%98%D7%92%D7%95%D7%A8%D7%99%D7%94:%D7%9E%D7%A8%D7%97%D7%91%D7%99%D7%9D_%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%99%D7%9D_%D7%99%D7%97%D7%99%D7%93%D7%90%D7%99%D7%9D" title="קטגוריה:מרחבים טופולוגיים יחידאים">דוגמאות</a> </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%A7%D7%91%D7%95%D7%A6%D7%AA_%D7%A7%D7%A0%D7%98%D7%95%D7%A8" title="קבוצת קנטור">קבוצת קנטור</a> • <a href="/wiki/%D7%A2%D7%A7%D7%95%D7%9E%D7%AA_%D7%94%D7%A1%D7%99%D7%A0%D7%95%D7%A1_%D7%A9%D7%9C_%D7%94%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%9D" title="עקומת הסינוס של הטופולוגים">עקומת הסינוס של הטופולוגים</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%94%D7%9E%D7%A1%D7%A8%D7%A7" title="מרחב המסרק">מרחב המסרק</a> • <a href="/w/index.php?title=%D7%94%D7%99%D7%A9%D7%A8_%D7%94%D7%90%D7%A8%D7%95%D7%9A&action=edit&redlink=1" class="new" title="הישר הארוך (הדף אינו קיים)">הישר הארוך</a> • <a href="/wiki/%D7%9E%D7%99%D7%A9%D7%95%D7%A8_%D7%9E%D7%95%D7%A8" title="מישור מור">מישור מור</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%90%D7%95%D7%A8%D7%99%D7%A1%D7%95%D7%9F_%D7%90%D7%95%D7%A0%D7%99%D7%91%D7%A8%D7%A1%D7%9C%D7%99" title="מרחב אוריסון אוניברסלי">מרחב אוריסון אוניברסלי</a> </td></tr> <tr> <td style="background-color: #F2F3F4; text-align: right; font-weight: bold; padding-left: 5px;">שונות </td> <td style="padding-right: 5px; text-align: right;"><a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%97%D7%9C%D7%A9%D7%94" title="טופולוגיה חלשה">טופולוגיה חלשה</a> • <a href="/w/index.php?title=%D7%AA%D7%9B%D7%95%D7%A0%D7%94_%D7%9E%D7%A7%D7%95%D7%9E%D7%99%D7%AA&action=edit&redlink=1" class="new" title="תכונה מקומית (הדף אינו קיים)">תכונה מקומית</a> • <a href="/wiki/%D7%90%D7%9C%D7%95%D7%9E%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="אלומה (מתמטיקה)">אלומה</a> • <a href="/wiki/%D7%9E%D7%A8%D7%97%D7%91_%D7%9B%D7%99%D7%A1%D7%95%D7%99" title="מרחב כיסוי">מרחב כיסוי</a> </td></tr> <tr> <td colspan="3" style="background-color: #F2F3F4; text-align: center; font-weight: bold;"><hr /> <p>נושאים ב<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>: <a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%A7%D7%91%D7%95%D7%A6%D7%AA%D7%99%D7%AA" title="טופולוגיה קבוצתית">טופולוגיה קבוצתית</a> • <a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%99%D7%AA" title="טופולוגיה אלגברית">טופולוגיה אלגברית</a> • <a href="/w/index.php?title=%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA&action=edit&redlink=1" class="new" title="טופולוגיה גאומטרית (הדף אינו קיים)">טופולוגיה גאומטרית</a> </p> <hr /> <p>נושאים ב<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>: <a href="/wiki/%D7%97%D7%A9%D7%91%D7%95%D7%9F_%D7%90%D7%99%D7%A0%D7%A4%D7%99%D7%A0%D7%99%D7%98%D7%A1%D7%99%D7%9E%D7%9C%D7%99" title="חשבון אינפיניטסימלי">חשבון אינפיניטסימלי</a> (<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_-_%D7%9E%D7%95%D7%A0%D7%97%D7%99%D7%9D" title="אנליזה מתמטית - מונחים">מונחון</a>) • <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%95%D7%A7%D7%98%D7%95%D7%A8%D7%99%D7%AA" title="אנליזה וקטורית">אנליזה וקטורית</a> • <a href="/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA" title="משוואה דיפרנציאלית">משוואות דיפרנציאליות</a> <a href="/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA_%D7%A8%D7%92%D7%99%D7%9C%D7%94" title="משוואה דיפרנציאלית רגילה">רגילות</a> <a href="/wiki/%D7%9E%D7%A9%D7%95%D7%95%D7%90%D7%94_%D7%93%D7%99%D7%A4%D7%A8%D7%A0%D7%A6%D7%99%D7%90%D7%9C%D7%99%D7%AA_%D7%97%D7%9C%D7%A7%D7%99%D7%AA" title="משוואה דיפרנציאלית חלקית">וחלקיות</a> • <a href="/wiki/%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%A7%D7%91%D7%95%D7%A6%D7%AA%D7%99%D7%AA" title="טופולוגיה קבוצתית">טופולוגיה קבוצתית</a> <a href="/w/index.php?title=%D7%98%D7%95%D7%A4%D7%95%D7%9C%D7%95%D7%92%D7%99%D7%94_%D7%92%D7%90%D7%95%D7%9E%D7%98%D7%A8%D7%99%D7%AA&action=edit&redlink=1" class="new" title="טופולוגיה גאומטרית (הדף אינו קיים)">וגאומטרית</a> • <a href="/wiki/%D7%90%D7%A0%D7%9C%D7%99%D7%96%D7%94_%D7%9E%D7%A8%D7%95%D7%9B%D7%91%D7%AA" title="אנליזה מרוכבת">אנליזה מרוכבת</a> • <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> • <a href="/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%9E%D7%99%D7%93%D7%94" title="תורת המידה">תורת המידה</a> </p> <hr /> </td></tr> </tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">אוחזר מתוך "<a dir="ltr" href="https://he.wikipedia.org/w/index.php?title=סגור_(טופולוגיה)&oldid=39177009">https://he.wikipedia.org/w/index.php?title=סגור_(טופולוגיה)&oldid=39177009</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a 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