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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Кіру</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"> Шыққан өңдеушілерге арналған беттер <a href="/wiki/%D0%96%D3%99%D1%80%D0%B4%D0%B5%D0%BC:%D0%A2%D0%B0%D0%BD%D1%8B%D1%81%D1%82%D1%8B%D1%80%D1%83" aria-label="Өңдеу туралы көбірек білу"><span>көбірек білу</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/%D0%90%D1%80%D0%BD%D0%B0%D0%B9%D1%8B:%D2%AE%D0%BB%D0%B5%D1%81%D1%96%D0%BC" title="Бұл IP мекенжаймен жасаған өңдемелер тізімі [y]" accesskey="y"><span>Үлесім</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%90%D1%80%D0%BD%D0%B0%D0%B9%D1%8B:%D0%A2%D0%B0%D0%BB%D2%9B%D1%8B%D0%BB%D0%B0%D1%83%D1%8B%D0%BC" title="Бұл IP мекенжай өңдемелерін 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<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="Мазмұнды көрсету/жасыру" > <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">Мазмұнды көрсету/жасыру</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">Изоморфизм (Математика)</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="Басқа тілдегі мақалаға өту. 59 тілде қолжетімді" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-59" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">59 тіл</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D9%85%D8%A7%D9%83%D9%84" title="تماكل – араб тілі" lang="ar" hreflang="ar" data-title="تماكل" data-language-autonym="العربية" data-language-local-name="араб тілі" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Isomorfismu" title="Isomorfismu – астурия тілі" lang="ast" hreflang="ast" data-title="Isomorfismu" data-language-autonym="Asturianu" data-language-local-name="астурия тілі" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C4%B0zomorfluq" title="İzomorfluq – әзірбайжан тілі" lang="az" hreflang="az" data-title="İzomorfluq" data-language-autonym="Azərbaycanca" data-language-local-name="әзірбайжан тілі" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC" title="Изоморфизм – башқұрт тілі" lang="ba" hreflang="ba" data-title="Изоморфизм" data-language-autonym="Башҡортса" data-language-local-name="башқұрт тілі" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%B7%D0%B0%D0%BC%D0%B0%D1%80%D1%84%D1%96%D0%B7%D0%BC" title="Ізамарфізм – беларусь тілі" lang="be" hreflang="be" data-title="Ізамарфізм" data-language-autonym="Беларуская" data-language-local-name="беларусь тілі" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D1%8A%D0%BC" title="Изоморфизъм – болгар тілі" lang="bg" hreflang="bg" data-title="Изоморфизъм" data-language-autonym="Български" data-language-local-name="болгар тілі" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Izomorfizam" title="Izomorfizam – босния тілі" lang="bs" hreflang="bs" data-title="Izomorfizam" data-language-autonym="Bosanski" data-language-local-name="босния тілі" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Isomorfisme" title="Isomorfisme – каталан тілі" lang="ca" hreflang="ca" data-title="Isomorfisme" data-language-autonym="Català" data-language-local-name="каталан тілі" 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/Izomorfismus" title="Izomorfismus – чех тілі" lang="cs" hreflang="cs" data-title="Izomorfismus" data-language-autonym="Čeština" data-language-local-name="чех тілі" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Isomorffedd" title="Isomorffedd – валлий тілі" lang="cy" hreflang="cy" data-title="Isomorffedd" data-language-autonym="Cymraeg" data-language-local-name="валлий тілі" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Isomorfi" title="Isomorfi – дат тілі" lang="da" hreflang="da" data-title="Isomorfi" data-language-autonym="Dansk" data-language-local-name="дат тілі" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Isomorphismus" title="Isomorphismus – неміс тілі" lang="de" hreflang="de" data-title="Isomorphismus" data-language-autonym="Deutsch" data-language-local-name="неміс тілі" 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%99%CF%83%CE%BF%CE%BC%CE%BF%CF%81%CF%86%CE%B9%CF%83%CE%BC%CF%8C%CF%82" title="Ισομορφισμός – грек тілі" lang="el" hreflang="el" data-title="Ισομορφισμός" data-language-autonym="Ελληνικά" data-language-local-name="грек тілі" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Isomorphism" title="Isomorphism – ағылшын тілі" lang="en" hreflang="en" data-title="Isomorphism" data-language-autonym="English" data-language-local-name="ағылшын тілі" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Izomorfio" title="Izomorfio – эсперанто тілі" lang="eo" hreflang="eo" data-title="Izomorfio" data-language-autonym="Esperanto" data-language-local-name="эсперанто тілі" 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/Isomorfismo" title="Isomorfismo – испан тілі" lang="es" hreflang="es" data-title="Isomorfismo" data-language-autonym="Español" data-language-local-name="испан тілі" 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/Isomorfism" title="Isomorfism – эстон тілі" lang="et" hreflang="et" data-title="Isomorfism" data-language-autonym="Eesti" data-language-local-name="эстон тілі" 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/Isomorfismo" title="Isomorfismo – баск тілі" lang="eu" hreflang="eu" data-title="Isomorfismo" data-language-autonym="Euskara" data-language-local-name="баск тілі" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DB%8C%DA%A9%D8%B1%DB%8C%D8%AE%D8%AA%DB%8C" title="یکریختی – парсы тілі" lang="fa" hreflang="fa" data-title="یکریختی" data-language-autonym="فارسی" data-language-local-name="парсы тілі" 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/Isomorfismi" title="Isomorfismi – фин тілі" lang="fi" hreflang="fi" data-title="Isomorfismi" data-language-autonym="Suomi" data-language-local-name="фин тілі" 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/Isomorphisme" title="Isomorphisme – француз тілі" lang="fr" hreflang="fr" data-title="Isomorphisme" data-language-autonym="Français" data-language-local-name="француз тілі" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Iseamorfacht" title="Iseamorfacht – ирланд тілі" lang="ga" hreflang="ga" data-title="Iseamorfacht" data-language-autonym="Gaeilge" data-language-local-name="ирланд тілі" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Isomorfismo" title="Isomorfismo – галисия тілі" lang="gl" hreflang="gl" data-title="Isomorfismo" data-language-autonym="Galego" data-language-local-name="галисия тілі" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/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 – иврит тілі" lang="he" hreflang="he" data-title="איזומורפיזם" data-language-autonym="עברית" data-language-local-name="иврит тілі" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Izomorfizam" title="Izomorfizam – хорват тілі" lang="hr" hreflang="hr" data-title="Izomorfizam" data-language-autonym="Hrvatski" data-language-local-name="хорват тілі" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Izomorfia" title="Izomorfia – венгр тілі" lang="hu" hreflang="hu" data-title="Izomorfia" data-language-autonym="Magyar" data-language-local-name="венгр тілі" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BB%D5%A6%D5%B8%D5%B4%D5%B8%D6%80%D6%86%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6_(%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1)" title="Իզոմորֆություն (մաթեմատիկա) – армян тілі" lang="hy" hreflang="hy" data-title="Իզոմորֆություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="армян тілі" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Isomorphismo" title="Isomorphismo – интерлингва тілі" lang="ia" hreflang="ia" data-title="Isomorphismo" data-language-autonym="Interlingua" data-language-local-name="интерлингва тілі" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Isomorfisme" title="Isomorfisme – индонезия тілі" lang="id" hreflang="id" data-title="Isomorfisme" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезия тілі" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Isomorfismo" title="Isomorfismo – итальян тілі" lang="it" hreflang="it" data-title="Isomorfismo" data-language-autonym="Italiano" data-language-local-name="итальян тілі" 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/%E5%90%8C%E5%9E%8B%E5%86%99%E5%83%8F" title="同型写像 – жапон тілі" lang="ja" hreflang="ja" data-title="同型写像" data-language-autonym="日本語" data-language-local-name="жапон тілі" 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/%EB%8F%99%ED%98%95_%EC%82%AC%EC%83%81" title="동형 사상 – корей тілі" lang="ko" hreflang="ko" data-title="동형 사상" data-language-autonym="한국어" data-language-local-name="корей тілі" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC" title="Изоморфизм – қырғыз тілі" lang="ky" hreflang="ky" data-title="Изоморфизм" data-language-autonym="Кыргызча" data-language-local-name="қырғыз тілі" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Isomorphismus" title="Isomorphismus – латын тілі" lang="la" hreflang="la" data-title="Isomorphismus" data-language-autonym="Latina" data-language-local-name="латын тілі" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Izomorfizmas" title="Izomorfizmas – литва тілі" lang="lt" hreflang="lt" data-title="Izomorfizmas" data-language-autonym="Lietuvių" data-language-local-name="литва тілі" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84" title="Изоморф – моңғол тілі" lang="mn" hreflang="mn" data-title="Изоморф" data-language-autonym="Монгол" data-language-local-name="моңғол тілі" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Isomorfisme" title="Isomorfisme – нидерланд тілі" lang="nl" hreflang="nl" data-title="Isomorfisme" data-language-autonym="Nederlands" data-language-local-name="нидерланд тілі" 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/Isomorfi" title="Isomorfi – норвегиялық нюнорск тілі" lang="nn" hreflang="nn" data-title="Isomorfi" data-language-autonym="Norsk nynorsk" data-language-local-name="норвегиялық нюнорск тілі" 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/Isomorfisme" title="Isomorfisme – норвегиялық букмол тілі" lang="nb" hreflang="nb" data-title="Isomorfisme" data-language-autonym="Norsk bokmål" data-language-local-name="норвегиялық букмол тілі" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%86%E0%A8%87%E0%A8%B8%E0%A9%8B%E0%A8%AE%E0%A9%8C%E0%A8%B0%E0%A8%AB%E0%A8%BF%E0%A8%9C%E0%A8%BC%E0%A8%AE" title="ਆਇਸੋਮੌਰਫਿਜ਼ਮ – пенджаб тілі" lang="pa" hreflang="pa" data-title="ਆਇਸੋਮੌਰਫਿਜ਼ਮ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="пенджаб тілі" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Izomorfizm" title="Izomorfizm – поляк тілі" lang="pl" hreflang="pl" data-title="Izomorfizm" data-language-autonym="Polski" data-language-local-name="поляк тілі" 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/Isomorfism" title="Isomorfism – Piedmontese" lang="pms" hreflang="pms" data-title="Isomorfism" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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/Isomorfismo" title="Isomorfismo – португал тілі" lang="pt" hreflang="pt" data-title="Isomorfismo" data-language-autonym="Português" data-language-local-name="португал тілі" 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/Izomorfism" title="Izomorfism – румын тілі" lang="ro" hreflang="ro" data-title="Izomorfism" data-language-autonym="Română" data-language-local-name="румын тілі" 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%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC" title="Изоморфизм – орыс тілі" lang="ru" hreflang="ru" data-title="Изоморфизм" data-language-autonym="Русский" data-language-local-name="орыс тілі" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Izomorfizam" title="Izomorfizam – серб-хорват тілі" lang="sh" hreflang="sh" data-title="Izomorfizam" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="серб-хорват тілі" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Isomorphism" title="Isomorphism – Simple English" lang="en-simple" hreflang="en-simple" data-title="Isomorphism" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Izomorfizem" title="Izomorfizem – словен тілі" lang="sl" hreflang="sl" data-title="Izomorfizem" data-language-autonym="Slovenščina" data-language-local-name="словен тілі" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%B0%D0%BC_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Изоморфизам (математика) – серб тілі" lang="sr" hreflang="sr" data-title="Изоморфизам (математика)" data-language-autonym="Српски / srpski" data-language-local-name="серб тілі" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Isomorfi" title="Isomorfi – швед тілі" lang="sv" hreflang="sv" data-title="Isomorfi" data-language-autonym="Svenska" data-language-local-name="швед тілі" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%90%E0%AE%9A%E0%AF%8B%E0%AE%AE%E0%AE%BE%E0%AE%B0%E0%AF%8D%E0%AE%AA%E0%AE%BF%E0%AE%B8%E0%AE%AE%E0%AF%8D" title="ஐசோமார்பிஸம் – тамил тілі" lang="ta" hreflang="ta" data-title="ஐசோமார்பிஸம்" data-language-autonym="தமிழ்" data-language-local-name="тамил тілі" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/%C4%B0zomorfizma" title="İzomorfizma – түрік тілі" lang="tr" hreflang="tr" data-title="İzomorfizma" data-language-autonym="Türkçe" data-language-local-name="түрік тілі" 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%86%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D1%96%D0%B7%D0%BC" title="Ізоморфізм – украин тілі" lang="uk" hreflang="uk" data-title="Ізоморфізм" data-language-autonym="Українська" data-language-local-name="украин тілі" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D8%B4%D8%A7%DA%A9%D9%84%D8%AA" title="مشاکلت – урду тілі" lang="ur" hreflang="ur" data-title="مشاکلت" data-language-autonym="اردو" data-language-local-name="урду тілі" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Izomorfizm_(matematika)" title="Izomorfizm (matematika) – өзбек тілі" lang="uz" hreflang="uz" data-title="Izomorfizm (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="өзбек тілі" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_%C4%91%E1%BA%B3ng_c%E1%BA%A5u" title="Phép đẳng cấu – вьетнам тілі" lang="vi" hreflang="vi" data-title="Phép đẳng cấu" data-language-autonym="Tiếng Việt" data-language-local-name="вьетнам тілі" 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%90%8C%E6%9E%84" title="同构 – қытай тілі (У)" lang="wuu" hreflang="wuu" data-title="同构" data-language-autonym="吴语" data-language-local-name="қытай тілі (У)" 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typeof="mw:File"><a href="/wiki/%D0%A1%D1%83%D1%80%D0%B5%D1%82:Disambig_gray.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/22px-Disambig_gray.svg.png" decoding="async" width="22" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/33px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/44px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span> Басқа мағыналар үшін <a href="/wiki/%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC" title="Изоморфизм">Изоморфизм</a> деген бетті қараңыз.</i></div> <p><b>Изоморфтық</b> — математикалық нысандардың (объектілердің) не нысандар жүйесінің арасындағы сәйкестікті (қатысты), кейбір жағдайда олардың құрылысының теңдігін де көрсететін негізгі ұғымдарының бірі. Математикада изоморфтық ұғымы нақты алгебралық жүйелерге (ең алдымен топқа) қолдануға байланысты қалыптасты. Кейін ол математикалық құрылымдардың кең класына (мысалы, сақина, өріс, т.б.) қолданыла бастады. Изоморфты жүйелердің қарапайым мысалы ретінде, қосу амалы (x=x<sub>1</sub>+x<sub>2</sub>), берілген барлық нақты сандар (R) жүйесі мен көбейту амалы (y=y<sub>1</sub>·y<sub>2</sub>), берілген оң сандар жүйесі (R+) қарастырылады. Осы екі жүйенің ішкі “құрылысы” бірдей болатындығын дәлелдеуге болады. Ол үшін, R-дің x санын R+-дің y=ax, (a>1) санына сәйкес қоя отырып, R жүйесін R+ жүйесіне бейнелеу жеткілікті. Сонда x=x<sub>1</sub>+x<sub>2</sub> сандарының қосындысы, x<sub>1</sub> және x<sub>2</sub> сандарына сәйкес келетін және сандарының y=y<sub>1</sub>·y<sub>2</sub> көбейтіндісіне сәйкес келеді. R+-дің R-ге кері бейнеленуінің түрі мынадай: x=log<sub>a</sub>y·R+ сандар жүйесінің қосындысына қатысты кез келген сөйлемнен оған сәйкес келетін R+ сандар жүйесінің көбейтіндісіне қатысты сөйлемді шығарып алуға болады. Мысалы, егер R-дегі <a href="/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BF%D1%80%D0%BE%D0%B3%D1%80%D0%B5%D1%81%D1%81%D0%B8%D1%8F" title="Арифметикалық прогрессия">арифметикалық прогрессия</a> мүшелерінің қосындысы (s<sub>n</sub>=x<sub>1</sub>+x<sub>2</sub>+...+x<sub>n</sub>) мына s<sub>n</sub>= формуласымен өрнектелсе, онда R+-дегі <a href="/w/index.php?title=%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D0%9F%D1%80%D0%BE%D0%B3%D1%80%D0%B5%D1%81%D1%81%D0%B8%D1%8F&action=edit&redlink=1" class="new" title="Геометриялық Прогрессия (мұндай бет жоқ)">геометриялық прогрессия</a> мүшелерінің көбейтіндісі (p<sub>n</sub>=y<sub>1</sub>·y<sub>2</sub>...y<sub>n</sub>) мына: p<sub>n</sub>= формуласымен өрнектеледі. Бұл жерде, R жүйесінен R+ жүйесіне ауысу кезінде: R-дегі n-ге көбейту амалы R+-дегі n-ге дәрежелеу амалына, ал екіге бөлу амалы квадрат түбір табу амалына сәйкес келеді. Топологияда маңызды рөл атқаратын гомеоморфтық ұғымы изоморфтық ұғымының дербес бір түрі болып есептеледі. Ал алгебралық жүйенің өзіне-өзінің изоморфтығы (бір мәнді бейнеленуі) автоморфтық деп аталады. “Изоморфтық” термині математикаға 19 ғасырдың ортасында енді. Оның қазіргі анықтамасы неміс математигі Э.Нeтердің (1882 – 1935) еңбектерінде қалыптасты.<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> </p> <div class="mw-heading mw-heading2"><h2 id="Дереккөздер"><span id=".D0.94.D0.B5.D1.80.D0.B5.D0.BA.D0.BA.D3.A9.D0.B7.D0.B4.D0.B5.D1.80"></span>Дереккөздер</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC_(%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&veaction=edit&section=1" title="Бөлімді өңдеу: Дереккөздер" class="mw-editsection-visualeditor"><span>өңдеу</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%98%D0%B7%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%B8%D0%B7%D0%BC_(%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)&action=edit&section=1" title="Бөлімнің қайнар кодын өңдеу: Дереккөздер"><span>қайнарын өңдеу</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">«Қазақстан»: Ұлттық энцклопедия / Бас редактор Ә. Нысанбаев – Алматы «<a href="/wiki/%D2%9A%D0%B0%D0%B7%D0%B0%D2%9B_%D1%8D%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F%D1%81%D1%8B" title="Қазақ энциклопедиясы">Қазақ энциклопедиясы»</a> Бас редакциясы, 1998 <a href="/wiki/%D0%90%D1%80%D0%BD%D0%B0%D0%B9%D1%8B:%D0%9A%D1%96%D1%82%D0%B0%D0%BF_%D2%9B%D0%B0%D0%B9%D0%BD%D0%B0%D1%80%D0%BB%D0%B0%D1%80%D1%8B/5898001239" class="internal mw-magiclink-isbn">ISBN 5-89800-123-9</a>, IV том</span> </li> </ol>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">«<a dir="ltr" href="https://kk.wikipedia.org/w/index.php?title=Изоморфизм_(Математика)&oldid=3306659">https://kk.wikipedia.org/w/index.php?title=Изоморфизм_(Математика)&oldid=3306659</a>» бетінен алынған</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%D0%90%D1%80%D0%BD%D0%B0%D0%B9%D1%8B:%D0%A1%D0%B0%D0%BD%D0%B0%D1%82%D1%82%D0%B0%D1%80" title="Арнайы:Санаттар">Санат</a>: <ul><li><a href="/wiki/%D0%A1%D0%B0%D0%BD%D0%B0%D1%82:%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Санат:Алгебра">Алгебра</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Жасырын санат: <ul><li><a href="/wiki/%D0%A1%D0%B0%D0%BD%D0%B0%D1%82:ISBN_%D1%81%D0%B8%D2%9B%D1%8B%D1%80%D0%BB%D1%8B_%D1%81%D1%96%D0%BB%D1%82%D0%B5%D0%BC%D0%B5%D0%BB%D0%B5%D1%80%D1%96_%D2%9B%D0%BE%D0%BB%D0%B4%D0%B0%D0%BD%D1%8B%D0%BB%D2%93%D0%B0%D0%BD_%D0%B1%D0%B5%D1%82%D1%82%D0%B5%D1%80" title="Санат:ISBN сиқырлы сілтемелері қолданылған беттер">ISBN сиқырлы сілтемелері қолданылған беттер</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Бұл беттің соңғы рет өзгертілген кезі: 2024 ж. сәуірдің 5, 21:16.</li> <li id="footer-info-copyright">Мәтін <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/">Creative Commons Attribution-ShareAlike лицензиясы</a> аясында қолжетімді; қосымша шарттар қолданылуы мүмкін. 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