<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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]).</p></abstract>

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]).

Sperner's Lemma

Institute of Informatics, University of Białystok, Poland

Formalized Mathematics

{"article-title":"Sperner's Lemma"}

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...

Sperner's Lemma

Online veröffentlicht: 05. Jan. 2011

Seitenbereich: 189 - 196

DOI: https://doi.org/10.2478/v10037-010-0022-x

This content is open access.