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2010 | 18 | 4 | 189-196
Tytuł artykułu

Sperner's Lemma

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).
Słowa kluczowe
Wydawca
Rocznik
Tom
18
Numer
4
Strony
189-196
Opis fizyczny
Daty
wydano
2010-01-01
online
2011-01-05
Twórcy
autor
  • Institute of Informatics, University of Białystok, Poland
Bibliografia
  • [1] Broderick Arneson and Piotr Rudnicki. Recognizing chordal graphs: Lex BFS and MCS. Formalized Mathematics, 14(4):187-205, 2006, doi:10.2478/v10037-006-0022-z.[Crossref]
  • [2] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [3] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [4] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [5] Grzegorz Bancerek and Yasunari Shidama. Introduction to matroids. Formalized Mathematics, 16(4):325-332, 2008, doi:10.2478/v10037-008-0040-0.[Crossref]
  • [6] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [7] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [8] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [9] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
  • [10] Roman Duda. Wprowadzenie do topologii. PWN, 1986.
  • [11] Noboru Endou, Takashi Mitsuishi, and Yasunari Shidama. Convex sets and convex combinations. Formalized Mathematics, 11(1):53-58, 2003.
  • [12] Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
  • [13] Adam Naumowicz. On Segre's product of partial line spaces. Formalized Mathematics, 9(2):383-390, 2001.
  • [14] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  • [15] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [16] Karol Pąk. Affine independence in vector spaces. Formalized Mathematics, 18(1):87-93, 2010, doi: 10.2478/v10037-010-0012-z.[Crossref]
  • [17] Karol Pąk. Abstract simplicial complexes. Formalized Mathematics, 18(1):95-106, 2010, doi: 10.2478/v10037-010-0013-y.[Crossref]
  • [18] Karol Pąk. The geometric interior in real linear spaces. Formalized Mathematics, 18(3):185-188, 2010, doi: 10.2478/v10037-010-0021-y.[Crossref]
  • [19] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [20] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [22] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [23] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-010-0022-x
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