About: Knaster–Kuratowski–Mazurkiewicz lemma

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The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem.

Attributes	Values
rdf:type	yago:WikicatLemmas yago:Abstraction100002137 yago:Communication100033020 yago:Lemma106751833 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453
rdfs:label	Lemme de Knaster-Kuratowski-Mazurkiewicz (fr) Knaster–Kuratowski–Mazurkiewicz lemma (en) 크나스테르-쿠라토프스키-마주르키에비치 덮개 (ko)
rdfs:comment	The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. (en) En mathématiques, et plus précisément en topologie algébrique, le lemme de Knaster-Kuratowski-Mazurkiewicz, ou lemme KKM, est un résultat de point fixe publié en 1929 par Bronisław Knaster, Kazimierz Kuratowski et Stefan Mazurkiewicz. (fr) 수학에서 크나스테르-쿠라토프스키-마주르키에비치 덮개(Knaster-Kuratowski-Mazurkiewicz덮개, 영어: Knaster–Kuratowski–Mazurkiewicz cover)는 특정한 조건을 만족시키는, 단체의 닫힌집합으로 구성된 덮개이다. 구체적으로, 단체의 (꼭짓점의 부분 집합의 볼록 폐포인) 부분 단체는 각 꼭짓점에 대응되는 닫힌집합들로 덮혀져야 한다. 크나스테르-쿠라토프스키-마주르키에비치 정리(Knaster-Kuratowski-Mazurkiewicz定理, 영어: Knaster–Kuratowski–Mazurkiewicz theorem)에 따르면, 모든 크나스테르-쿠라토프스키-마주르키에비치 덮개는 적어도 하나 이상의 점을 공유한다 (즉, 그 교집합은 공집합이 될 수 없다). (ko)
foaf:depiction
dcterms:subject	Lemmas Fixed points (mathematics)
Wikipage page ID	3963004 (xsd:integer)
Wikipage revision ID	1060556447 (xsd:integer)
Link from a Wikipage to another Wikipage	Barycenter David Gale Lemmas Fixed points (mathematics) Matching in hypergraphs Closed sets Convex combination Convex hull Cooperative game theory Lloyd Shapley Simplex Stefan Mazurkiewicz Closed set Ravindra Bapat Bronisław Knaster Economics Fixed-point theorem Brouwer fixed-point theorem Carathéodory's theorem (convex hull) Cover (topology) Kazimierz Kuratowski Homotopy Sperner's lemma Open set Vertex (geometry) Polytope Connected set dbr:Hidetoshi_Komiya
Link from a Wikipage to an external page	https://planetmath.org/kkmlemma
sameAs	Knaster–Kuratowski–Mazurkiewicz lemma Knaster–Kuratowski–Mazurkiewicz lemma Knaster–Kuratowski–Mazurkiewicz lemma Knaster–Kuratowski–Mazurkiewicz lemma Knaster–Kuratowski–Mazurkiewicz lemma Knaster–Kuratowski–Mazurkiewicz lemma
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thumbnail	wiki-commons:Special:FilePath/KKM_example.png?width=300
has abstract	The Knaster–Kuratowski–Mazurkiewicz lemma is a basic result in mathematical fixed-point theory published in 1929 by Knaster, Kuratowski and Mazurkiewicz. The KKM lemma can be proved from Sperner's lemma and can be used to prove the Brouwer fixed-point theorem. (en) En mathématiques, et plus précisément en topologie algébrique, le lemme de Knaster-Kuratowski-Mazurkiewicz, ou lemme KKM, est un résultat de point fixe publié en 1929 par Bronisław Knaster, Kazimierz Kuratowski et Stefan Mazurkiewicz. (fr) 수학에서 크나스테르-쿠라토프스키-마주르키에비치 덮개(Knaster-Kuratowski-Mazurkiewicz덮개, 영어: Knaster–Kuratowski–Mazurkiewicz cover)는 특정한 조건을 만족시키는, 단체의 닫힌집합으로 구성된 덮개이다. 구체적으로, 단체의 (꼭짓점의 부분 집합의 볼록 폐포인) 부분 단체는 각 꼭짓점에 대응되는 닫힌집합들로 덮혀져야 한다. 크나스테르-쿠라토프스키-마주르키에비치 정리(Knaster-Kuratowski-Mazurkiewicz定理, 영어: Knaster–Kuratowski–Mazurkiewicz theorem)에 따르면, 모든 크나스테르-쿠라토프스키-마주르키에비치 덮개는 적어도 하나 이상의 점을 공유한다 (즉, 그 교집합은 공집합이 될 수 없다). (ko)
gold:hypernym	Result
prov:wasDerivedFrom	wikipedia-en:Knaster–Kuratowski–Mazurkiewicz_lemma?oldid=1060556447&ns=0
page length (characters) of wiki page	14865 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Knaster–Kuratowski–Mazurkiewicz_lemma
is Link from a Wikipage to another Wikipage of	List of lemmas Envy-freeness Core (game theory) Bronisław Knaster KKMS theorem KKMS lemma Kazimierz Kuratowski Efficient envy-free division Sperner's lemma Greedy embedding KKM KKMS Knaster-Kuratowski-Mazurkiewicz lemma Komiya's theorem KKM lemma K-K-M lemma K-k-m lemma K-k-m theorem
is Wikipage redirect of	KKMS theorem KKMS lemma Knaster-Kuratowski-Mazurkiewicz lemma Komiya's theorem KKM lemma K-K-M lemma K-k-m lemma K-k-m theorem
is known for of	Bronisław Knaster

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