Sperner lemma  is probably one of the most elegant and fundamental results in combinatorial topology. As we have seen, this lemma provides a very important geometric background for developing simplicial methods. Recall this lemma states that given a simplicial subdivision of the unit simplex S n and a labeling function L from the set of vertices of simplices of the simplicial subdivision into the set I n , there exists a completely labeled simplex, if x i = 0 implies that L(x)≠ i for any vertex x ∈ S n .
KeywordsUnit Simplex Proper Face Label Rule Combinatorial Topology Simplicial Subdivision
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