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Disponibil în 35 limbi" > <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-35" 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">35 limbi</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/%D9%81%D8%B6%D8%A7%D8%A1_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="فضاء رياضي – arabă" lang="ar" hreflang="ar" data-title="فضاء رياضي" data-language-autonym="العربية" data-language-local-name="arabă" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D0%B0%D1%81%D1%82%D0%BE%D1%80%D0%B0_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Прастора (матэматыка) – belarusă" lang="be" hreflang="be" data-title="Прастора (матэматыка)" data-language-autonym="Беларуская" data-language-local-name="belarusă" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Espai_(matem%C3%A0tiques)" title="Espai (matemàtiques) – catalană" lang="ca" hreflang="ca" data-title="Espai (matemàtiques)" data-language-autonym="Català" data-language-local-name="catalană" 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/Prostor_(matematika)" title="Prostor (matematika) – cehă" lang="cs" hreflang="cs" data-title="Prostor (matematika)" data-language-autonym="Čeština" data-language-local-name="cehă" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A3%C3%A7%D0%BB%C4%83%D1%85_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Уçлăх (математика) – ciuvașă" lang="cv" hreflang="cv" data-title="Уçлăх (математика)" data-language-autonym="Чӑвашла" data-language-local-name="ciuvașă" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Raum_(Mathematik)" title="Raum (Mathematik) – germană" lang="de" hreflang="de" data-title="Raum (Mathematik)" data-language-autonym="Deutsch" data-language-local-name="germană" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A7%CF%8E%CF%81%CE%BF%CF%82_(%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC)" title="Χώρος (μαθηματικά) – greacă" lang="el" hreflang="el" data-title="Χώρος (μαθηματικά)" data-language-autonym="Ελληνικά" data-language-local-name="greacă" 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/Space_(mathematics)" title="Space (mathematics) – engleză" lang="en" hreflang="en" data-title="Space (mathematics)" data-language-autonym="English" data-language-local-name="engleză" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Ruum_(matemaatika)" title="Ruum (matemaatika) – estonă" lang="et" hreflang="et" data-title="Ruum (matemaatika)" data-language-autonym="Eesti" data-language-local-name="estonă" 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/Espazio_(matematika)" title="Espazio (matematika) – bască" lang="eu" hreflang="eu" data-title="Espazio (matematika)" data-language-autonym="Euskara" data-language-local-name="bască" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B6%D8%A7_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="فضا (ریاضیات) – persană" lang="fa" hreflang="fa" data-title="فضا (ریاضیات)" data-language-autonym="فارسی" data-language-local-name="persană" 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/Avaruus_(matematiikka)" title="Avaruus (matematiikka) – finlandeză" lang="fi" hreflang="fi" data-title="Avaruus (matematiikka)" data-language-autonym="Suomi" data-language-local-name="finlandeză" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A8%D7%97%D7%91_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="מרחב (מתמטיקה) – ebraică" lang="he" hreflang="he" data-title="מרחב (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="ebraică" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D5%A1%D6%80%D5%A1%D5%AE%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="Տարածություն (մաթեմատիկա) – armeană" lang="hy" hreflang="hy" data-title="Տարածություն (մաթեմատիկա)" data-language-autonym="Հայերեն" data-language-local-name="armeană" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ruang_(matematika)" title="Ruang (matematika) – indoneziană" lang="id" hreflang="id" data-title="Ruang (matematika)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indoneziană" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Spaco_(matematiko)" title="Spaco (matematiko) – ido" lang="io" hreflang="io" data-title="Spaco (matematiko)" data-language-autonym="Ido" data-language-local-name="ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Spazio_(matematica)" title="Spazio (matematica) – italiană" lang="it" hreflang="it" data-title="Spazio (matematica)" data-language-autonym="Italiano" data-language-local-name="italiană" 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/%E7%A9%BA%E9%96%93_(%E6%95%B0%E5%AD%A6)" title="空間 (数学) – japoneză" lang="ja" hreflang="ja" data-title="空間 (数学)" data-language-autonym="日本語" data-language-local-name="japoneză" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9A%D0%B5%D2%A3%D1%96%D1%81%D1%82%D1%96%D0%BA_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Кеңістік (математика) – kazahă" lang="kk" hreflang="kk" data-title="Кеңістік (математика)" data-language-autonym="Қазақша" data-language-local-name="kazahă" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%B5%EA%B0%84_(%EC%88%98%ED%95%99)" title="공간 (수학) – coreeană" lang="ko" hreflang="ko" data-title="공간 (수학)" data-language-autonym="한국어" data-language-local-name="coreeană" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Ruang_(matematik)" title="Ruang (matematik) – malaeză" lang="ms" hreflang="ms" data-title="Ruang (matematik)" data-language-autonym="Bahasa Melayu" data-language-local-name="malaeză" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ruimte_(wiskunde)" title="Ruimte (wiskunde) – neerlandeză" lang="nl" hreflang="nl" data-title="Ruimte (wiskunde)" data-language-autonym="Nederlands" data-language-local-name="neerlandeză" 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/Rom_i_matematikk" title="Rom i matematikk – norvegiană nynorsk" lang="nn" hreflang="nn" data-title="Rom i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegiană nynorsk" 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/Rom_(matematikk)" title="Rom (matematikk) – norvegiană bokmål" lang="nb" hreflang="nb" data-title="Rom (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norvegiană bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Spatie" title="Spatie – Novial" lang="nov" hreflang="nov" data-title="Spatie" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%B8%E0%A8%AA%E0%A9%87%E0%A8%B8_(%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4)" title="ਸਪੇਸ (ਗਣਿਤ) – punjabi" lang="pa" hreflang="pa" data-title="ਸਪੇਸ (ਗਣਿਤ)" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Przestrze%C5%84_(matematyka)" title="Przestrzeń (matematyka) – poloneză" lang="pl" hreflang="pl" data-title="Przestrzeń (matematyka)" data-language-autonym="Polski" data-language-local-name="poloneză" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Espa%C3%A7o_matem%C3%A1tico" title="Espaço matemático – portugheză" lang="pt" hreflang="pt" data-title="Espaço matemático" data-language-autonym="Português" data-language-local-name="portugheză" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%80%D0%B0%D0%BD%D1%81%D1%82%D0%B2%D0%BE_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Пространство (математика) – rusă" lang="ru" hreflang="ru" data-title="Пространство (математика)" data-language-autonym="Русский" data-language-local-name="rusă" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rum_(matematik)" title="Rum (matematik) – suedeză" lang="sv" hreflang="sv" data-title="Rum (matematik)" data-language-autonym="Svenska" data-language-local-name="suedeză" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Uzay_(matematik)" title="Uzay (matematik) – turcă" lang="tr" hreflang="tr" data-title="Uzay (matematik)" data-language-autonym="Türkçe" data-language-local-name="turcă" 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%9F%D1%80%D0%BE%D1%81%D1%82%D1%96%D1%80_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Простір (математика) – ucraineană" lang="uk" hreflang="uk" data-title="Простір (математика)" data-language-autonym="Українська" data-language-local-name="ucraineană" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Fazo_(matematika)" title="Fazo (matematika) – uzbecă" lang="uz" hreflang="uz" data-title="Fazo (matematika)" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbecă" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%A9%BA%E9%97%B4_(%E6%95%B0%E5%AD%A6)" title="空间 (数学) – chineză" lang="zh" hreflang="zh" data-title="空间 (数学)" data-language-autonym="中文" data-language-local-name="chineză" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%A9%BA%E9%96%93_(%E6%95%B8%E5%AD%B8)" title="空間 (數學) – cantoneză" lang="yue" hreflang="yue" data-title="空間 (數學)" data-language-autonym="粵語" data-language-local-name="cantoneză" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q472971#sitelinks-wikipedia" title="Modifică legăturile interlinguale" class="wbc-editpage">Modifică legăturile</a></span></div> </div> </div> </div> </header> <div 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href="/w/index.php?title=Special:QrKodu&url=https%3A%2F%2Fro.wikipedia.org%2Fwiki%2FSpa%25C8%259Biu_%28matematic%25C4%2583%29"><span>Descărcați codul QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tipărire/exportare </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Special:Carte&bookcmd=book_creator&referer=Spa%C8%9Biu+%28matematic%C4%83%29"><span>Creare carte</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=Spa%C8%9Biu_%28matematic%C4%83%29&action=show-download-screen"><span>Descărcare ca PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&printable=yes" title="Versiunea de tipărit a acestei pagini [p]" accesskey="p"><span>Versiune de tipărit</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> În alte proiecte </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Space_(mathematics)" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q472971" title="Legătură către elementul asociat din depozitul de date [g]" accesskey="g"><span>Element Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Aspect"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Aspect</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mută în bara laterală</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ascunde</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">De la Wikipedia, enciclopedia liberă</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ro" dir="ltr"><ul><li><i>Acest articol se referă la conceptul de <b>spațiu din <a href="/wiki/Matematic%C4%83" title="Matematică">matematică</a> și eventualele sale interpretările sale <a href="/wiki/Filozofie" class="mw-redirect" title="Filozofie">filozofice</a></b>.</i></li></ul> <p><i>Pentru alte sensuri, vedeți <a href="/wiki/Spa%C8%9Biu_(dezambiguizare)" class="mw-disambig" title="Spațiu (dezambiguizare)">Spațiu (dezambiguizare)</a></i>. </p><p><b>Spațiul</b>, în matematică, reprezintă o mulțime de elemente (puncte) cu anumite proprietăți. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Definiții"><span id="Defini.C8.9Bii"></span>Definiții</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&veaction=edit&section=1" title="Modifică secțiunea: Definiții" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&action=edit&section=1" title="Edit section's source code: Definiții"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Spa%C8%9Biu_metric" title="Spațiu metric">Spațiu metric</a>, o <a href="/wiki/Mul%C8%9Bime" title="Mulțime">mulțime</a> pe care este definită o funcție distanță;</li></ul> <ul><li><a href="/wiki/Spa%C8%9Biu_euclidian" title="Spațiu euclidian">Spațiu euclidian</a> (<b>real</b>) <b>n - dimensional</b>, <a href="/wiki/Mul%C8%9Bime" title="Mulțime">mulțime</a> ale cărei puncte se pot pune în corespondență biunivocă cu sistemele ordonate de <i>n</i> numere reale și în care s-a definit distanța <i>d</i> dintre două puncte <i>x</i> de coordonate (x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>) și respectiv <i>y</i> de coordonate (y<sub>1</sub>, y<sub>2</sub>, ..., y<sub>n</sub>) prin formula lui <a href="/wiki/Pitagora" title="Pitagora">Pitagora</a>:</li></ul> <div style="text-align:center"> <code> <p><i>d</i> ( <i>x</i> , <i>y</i> ) = <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ({({y_{1}}-{x_{1}})^{2}}+...+{({y_{n}}-{x_{n}})^{2}})^{\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>+</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({({y_{1}}-{x_{1}})^{2}}+...+{({y_{n}}-{x_{n}})^{2}})^{\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8634bde49fc873edebc76df39dd12047ada3664f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:31.154ex; height:4.009ex;" alt="{\displaystyle ({({y_{1}}-{x_{1}})^{2}}+...+{({y_{n}}-{x_{n}})^{2}})^{\frac {1}{2}}}"></span> </p> </code> </div> <ul><li><a href="/wiki/Spa%C8%9Biu_afin" title="Spațiu afin">Spațiu afin</a>, spațiu ale cărui proprietăți sunt invariante față de <a href="/w/index.php?title=Transformare_afin%C4%83&action=edit&redlink=1" class="new" title="Transformare afină — pagină inexistentă">transformările afine</a>.</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biu_proiectiv&action=edit&redlink=1" class="new" title="Spațiu proiectiv — pagină inexistentă">Spațiu proiectiv</a>, spațiu ale cărui proprietăți sunt invariante față de transformările proiective.</li></ul> <ul><li><a href="/wiki/Spa%C8%9Biu_vectorial" title="Spațiu vectorial">spațiu vectorial</a>, numit și <i>spațiu liniar</i>, modul peste un <a href="/wiki/Corp" class="mw-disambig" title="Corp">corp</a> de <a href="/wiki/Scalar" class="mw-disambig" title="Scalar">scalari</a>. Exemplu : mulțimea funcțiilor reale continue definite pe un interval [ <i>a</i>, <i>b</i> ], mulțimea matricilor pătrate de ordinul <i>n</i> sunt spații vectoriale peste corpul numerelor reale, complexe. Spațiile vectoriale au fost definite în forma actuală de <a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a> (<a href="/wiki/1888" title="1888">1888</a>), dar fondatorul spațiilor vectoriale rămâne <a href="/w/index.php?title=Hermann_Gunther_Grassmann&action=edit&redlink=1" class="new" title="Hermann Gunther Grassmann — pagină inexistentă">Hermann Gunther Grassmann</a> (<a href="/wiki/1844" title="1844">1844</a>).</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biu_vectorial_real&action=edit&redlink=1" class="new" title="Spațiu vectorial real — pagină inexistentă">Spațiu vectorial real</a>, spațiu vectorial (liniar) față de corpul <a href="/wiki/Num%C4%83r" title="Număr">numerelor</a> reale.</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biu_vectorial_complex&action=edit&redlink=1" class="new" title="Spațiu vectorial complex — pagină inexistentă">Spațiu vectorial complex</a> , spațiu vectorial (liniar) față de corpul <a href="/wiki/Num%C4%83r" title="Număr">numerelor</a> complexe.</li></ul> <ul><li><a href="/wiki/Spa%C8%9Biu_vectorial_normat" title="Spațiu vectorial normat">Spațiu vectorial normat</a>, spațiu vectorial, liniar sau complex, pe care este definită o <a href="/w/index.php?title=Norm%C4%83_(spa%C8%9Biu_normat)&action=edit&redlink=1" class="new" title="Normă (spațiu normat) — pagină inexistentă">normă (spațiu normat)</a>.</li> <li><a href="/wiki/Spa%C8%9Biu_Banach" title="Spațiu Banach">Spațiu vectorial normat complet</a>, numit și <i>spațiu Banach</i>, spațiu normat în care orice <a href="/wiki/%C8%98ir_Cauchy" title="Șir Cauchy">șir Cauchy</a> este <a href="/wiki/%C8%98ir_convergent" title="Șir convergent">convergent</a>.</li> <li><a href="/wiki/Spa%C8%9Biu_prehilbertian" title="Spațiu prehilbertian">Spațiu prehilbertian</a>, spațiu vectorial, liniar sau complex, pe care este definit un <a href="/wiki/Produs_scalar" title="Produs scalar">produs scalar</a>; produsul scalar induce o normă, astfel că orice spațiu prehilbertian este spațiu normat.</li> <li><a href="/wiki/Spa%C8%9Biu_Hilbert" title="Spațiu Hilbert">Spațiu Hilbert</a> - este un spațiu prehilbertian care este în același timp spațiu Banach, denumit astfel după matematicianul <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> (<a href="/wiki/1862" title="1862">1862</a>-<a href="/wiki/1943" title="1943">1943</a>).</li> <li><a href="/wiki/Spa%C8%9Biu_topologic" title="Spațiu topologic">Spațiu topologic</a> - este cel mai general cadru în care poate fi definită noțiunea de limită. Mulțimea numerelor reale, cu topologia formată din intervale deschise este un spațiu topologic, pe care noțiunile de limită și funcție continuă revin la cele din analiza funcțiilor reale de variabilă reală.</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biu_liniar_topologic&action=edit&redlink=1" class="new" title="Spațiu liniar topologic — pagină inexistentă">Spațiu liniar topologic</a> - spațiu liniar și topologic.</li></ul> <ul><li><a href="/wiki/Spa%C8%9Biu_func%C8%9Bional" title="Spațiu funcțional">Spațiu funcțional</a> - spațiu topologic ale cărui elemente sunt funcții. Cele mai importante spații funcționale sunt cele liniare.</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biul_lui_Riemann&action=edit&redlink=1" class="new" title="Spațiul lui Riemann — pagină inexistentă">Spațiul lui Riemann</a>, varietate diferențiabilă, dotată cu o lege de măsurare a lungimilor unor curbe</li></ul> <ul><li><a href="/w/index.php?title=Spa%C8%9Biu_conform&action=edit&redlink=1" class="new" title="Spațiu conform — pagină inexistentă">Spațiu conform</a> este un spațiu al lui Riemann având proprietatea că metrica sa, înmulțită cu o funcție depinzând de coordonate, devine metrica spațiului euclidian.</li></ul> <ul><li><a href="/wiki/Spa%C8%9Biu_Minkowski" title="Spațiu Minkowski">Spațiu Minkowski</a> (spațiu-timp) - spațiu cu patru dimensiuni ale cărui puncte corespund evenimentelor din <a href="/wiki/Teoria_relativit%C4%83%C8%9Bii_restr%C3%A2nse" title="Teoria relativității restrânse">teoria relativității restrânse</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Vezi_și"><span id="Vezi_.C8.99i"></span>Vezi și</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&veaction=edit&section=2" title="Modifică secțiunea: Vezi și" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&action=edit&section=2" title="Edit section's source code: Vezi și"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Geometrie_euclidian%C4%83" title="Geometrie euclidiană">Geometrie euclidiană</a></li> <li><a href="/wiki/Func%C8%9Bie" title="Funcție">Funcție</a></li> <li><a href="/wiki/List%C4%83_de_func%C8%9Bii_matematice" title="Listă de funcții matematice">Listă de funcții matematice</a></li> <li><a href="/wiki/List%C4%83_de_matematicieni" title="Listă de matematicieni">Listă de matematicieni</a></li> <li><a href="/wiki/Spa%C8%9Biu_vectorial" title="Spațiu vectorial">Spațiu vectorial</a></li> <li><a href="/wiki/Vector_(spa%C8%9Bial)" class="mw-redirect" title="Vector (spațial)">Vector (spațial)</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Bibliografie">Bibliografie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&veaction=edit&section=3" title="Modifică secțiunea: Bibliografie" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&action=edit&section=3" title="Edit section's source code: Bibliografie"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i>Dicționar de matematici generale</i>, Ed enciclopedică română, București, 1974</li> <li><i>Mică enciclopedie matematică</i>, Editura Tehnică, București, 1980.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Legături_externe"><span id="Leg.C4.83turi_externe"></span>Legături externe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&veaction=edit&section=4" title="Modifică secțiunea: Legături externe" class="mw-editsection-visualeditor"><span>modificare</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Spa%C8%9Biu_(matematic%C4%83)&action=edit&section=4" title="Edit section's source code: Legături externe"><span>modificare sursă</span></a><span class="mw-editsection-bracket">]</span></span></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Adus de la <a dir="ltr" href="https://ro.wikipedia.org/w/index.php?title=Spațiu_(matematică)&oldid=14671838">https://ro.wikipedia.org/w/index.php?title=Spațiu_(matematică)&oldid=14671838</a></div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:Categorii" title="Special:Categorii">Categorie</a>: <ul><li><a href="/wiki/Categorie:Matematic%C4%83" title="Categorie:Matematică">Matematică</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"> Ultima editare a paginii a fost efectuată la 2 decembrie 2021, ora 19:53.</li> <li id="footer-info-copyright">Acest text este disponibil sub licența <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ro">Creative Commons cu atribuire și distribuire în condiții identice</a>; pot exista și clauze suplimentare. 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