Sperner's Lemma

Karol Pąk
2010 Formalized Mathematics  
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 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]).
doi:10.2478/v10037-010-0022-x fatcat:thkotoqgx5b2jl5ife23ftuxiq