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]).
@article{bwmeta1.element.doi-10_2478_v10037-010-0022-x,
author = {Karol P\k ak},
title = {Sperner's Lemma},
journal = {Formalized Mathematics},
volume = {18},
year = {2010},
pages = {189-196},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0022-x}
}
Karol Pąk. Sperner's Lemma. Formalized Mathematics, Tome 18 (2010) pp. 189-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10037-010-0022-x/
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