Sperner's Lemma

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 f, 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 f(S) = K (see [10]). © 2010 University of Białystok.