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About: Invariance of domain
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title="Switch to /sparql endpoint"><i class="bi-box-arrow-up-right"></i> Sparql Endpoint </a> </li> </ul> </div> </div> </nav> <div style="margin-bottom: 60px"></div> <!-- /navbar --> <!-- page-header --> <section> <div class="container-xl"> <div class="row"> <div class="col"> <h1 id="title" class="display-6"><b>About:</b> <a href="http://dbpedia.org/resource/Invariance_of_domain">Invariance of domain</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> <span class="text-nowrap">An Entity of Type: <a href="http://dbpedia.org/class/yago/WikicatTheoremsInTopology">WikicatTheoremsInTopology</a>, </span> <span class="text-nowrap">from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, </span> <span class="text-nowrap">within Data Space: <a href="http://dbpedia.org">dbpedia.org</a></span> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> <p class="lead">Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space . It states: If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and . The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.</p> </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/A_map_which_is_not_a_homeomorphism_onto_its_image.png?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section> <!-- page-header --> <!-- property-table --> <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract"><small>dbo:</small>abstract</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:abstract" lang="en" >Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space . It states: If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and . The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="es" >La invarianza del dominio es un teorema topológico sobre subconjuntos homeomórficos de un espacio euclídeo Rn. Afirma que: El teorema y su demostración, publicados en 1912, se deben a Luitzen Egbertus Jan Brouwer. La demostración utiliza herramientas de topología algebraica, en especial el teorema del punto fijo de Brouwer.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="fr" >En mathématiques, et plus précisément en topologie, le théorème de l'invariance du domaine est un résultat dû à L. E. J. Brouwer (1912), concernant les applications continues entre sous-ensembles de Rn.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="pl" >Twierdzenie Brouwera o zachowaniu otwartości – twierdzenie topologii sformułowane i udowodnione w 1912 przez Jana Brouwera. Mówi ono, że podzbiór przestrzeni euklidesowej homeomorficzny z podzbiorem otwartym tej przestrzeni jest jej podzbiorem otwartym. Brouwer użył w dowodzie wprowadzonych przez siebie metod topologii algebraicznej, a w szczególności twierdzenia Brouwera o punkcie stałym. Twierdzenie to bywa również nazywane twierdzeniem o niezmienniczości obszaru (ang. Invariance of Domain).</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="ru" >Теорема об инвариантности области утверждает, что образ непрерывного инъективного отображения Евклидова пространства в себя открыт.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="dbo:abstract" lang="uk" >Теорема про інваріантність областей стверджує, що образ відкритої підмножини евклідового простору при неперервному ін'єктивному відображенні у цей же евклідів простір є відкритою множиною. Теорема була доведена Лейтзеном Брауером.</span><small> (uk)</small></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail"><small>dbo:</small>thumbnail</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/A_map_which_is_not_a_homeomorphism_onto_its_image.png?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/A_map_which_is_not_a_homeomorphism_onto_its_image.png?width=300"><small>wiki-commons</small>:Special:FilePath/A_map_which_is_not_a_homeomorphism_onto_its_image.png?width=300</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink"><small>dbo:</small>wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://link.springer.com/article/10.1007%2FBF02568096" href="https://link.springer.com/article/10.1007%2FBF02568096">https://link.springer.com/article/10.1007%2FBF02568096</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://terrytao.wordpress.com/2011/06/13/brouwers-fixed-point-and-invariance-of-domain-theorems-and-hilberts-fifth-problem/%7Ctitle=Brouwer%E2%80%99s" href="http://terrytao.wordpress.com/2011/06/13/brouwers-fixed-point-and-invariance-of-domain-theorems-and-hilberts-fifth-problem/%7Ctitle=Brouwer%E2%80%99s">http://terrytao.wordpress.com/2011/06/13/brouwers-fixed-point-and-invariance-of-domain-theorems-and-hilberts-fifth-problem/%7Ctitle=Brouwer%E2%80%99s</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="http://dml.cz/bitstream/handle/10338.dmlcz/702050/ActaCarolinae_039-1998-1_10.pdf%7Cmr=1696596" href="http://dml.cz/bitstream/handle/10338.dmlcz/702050/ActaCarolinae_039-1998-1_10.pdf%7Cmr=1696596">http://dml.cz/bitstream/handle/10338.dmlcz/702050/ActaCarolinae_039-1998-1_10.pdf%7Cmr=1696596</a></span></li> <li><span class="literal"><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://archive.org/details/in.ernet.dli.2015.84609/" href="https://archive.org/details/in.ernet.dli.2015.84609/">https://archive.org/details/in.ernet.dli.2015.84609/</a></span></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageID"><small>dbo:</small>wikiPageID</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="dbo:wikiPageID" datatype="xsd:integer" >210731</span><small> (xsd:integer)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageLength"><small>dbo:</small>wikiPageLength</a> </td><td class="col-10 text-break"><ul> 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href="http://dbpedia.org/class/yago/Statement106722453"><small>yago</small>:Statement106722453</a></span></li> <li><span class="literal"><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/Theorem106752293" href="http://dbpedia.org/class/yago/Theorem106752293"><small>yago</small>:Theorem106752293</a></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment"><small>rdfs:</small>comment</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><span property="rdfs:comment" lang="en" >Invariance of domain is a theorem in topology about homeomorphic subsets of Euclidean space . It states: If is an open subset of and is an injective continuous map, then is open in and is a homeomorphism between and . The theorem and its proof are due to L. E. J. Brouwer, published in 1912. The proof uses tools of algebraic topology, notably the Brouwer fixed point theorem.</span><small> (en)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="es" >La invarianza del dominio es un teorema topológico sobre subconjuntos homeomórficos de un espacio euclídeo Rn. Afirma que: El teorema y su demostración, publicados en 1912, se deben a Luitzen Egbertus Jan Brouwer. La demostración utiliza herramientas de topología algebraica, en especial el teorema del punto fijo de Brouwer.</span><small> (es)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="fr" >En mathématiques, et plus précisément en topologie, le théorème de l'invariance du domaine est un résultat dû à L. E. J. Brouwer (1912), concernant les applications continues entre sous-ensembles de Rn.</span><small> (fr)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="pl" >Twierdzenie Brouwera o zachowaniu otwartości – twierdzenie topologii sformułowane i udowodnione w 1912 przez Jana Brouwera. Mówi ono, że podzbiór przestrzeni euklidesowej homeomorficzny z podzbiorem otwartym tej przestrzeni jest jej podzbiorem otwartym. Brouwer użył w dowodzie wprowadzonych przez siebie metod topologii algebraicznej, a w szczególności twierdzenia Brouwera o punkcie stałym. Twierdzenie to bywa również nazywane twierdzeniem o niezmienniczości obszaru (ang. Invariance of Domain).</span><small> (pl)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="ru" >Теорема об инвариантности области утверждает, что образ непрерывного инъективного отображения Евклидова пространства в себя открыт.</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:comment" lang="uk" >Теорема про інваріантність областей стверджує, що образ відкритої підмножини евклідового простору при неперервному ін'єктивному відображенні у цей же евклідів простір є відкритою множиною. 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области</span><small> (ru)</small></span></li> <li style="display:none;"><span class="literal"><span property="rdfs:label" lang="uk" >Теорема Брауера про інваріантність областей</span><small> (uk)</small></span></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs"><small>owl:</small>sameAs</a> </td><td class="col-10 text-break"><ul> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://rdf.freebase.com/ns/m.01dxws" href="http://rdf.freebase.com/ns/m.01dxws"><small>freebase</small>:Invariance of domain</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://yago-knowledge.org/resource/Invariance_of_domain" href="http://yago-knowledge.org/resource/Invariance_of_domain"><small>yago-res</small>:Invariance of domain</a></span></li> <li><span class="literal"><a class="uri" rel="owl:sameAs" resource="http://www.wikidata.org/entity/Q3527201" 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