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Combinatorial lemmas for nonoriented pseudomanifolds. (English) Zbl 1038.05010

Summary: Sperner lemma type theorems are proved for nonoriented primoids and pseudomanifolds. A rank function of a primoid is defined. Applications of these theorems to the geometric simplex are given. Also Knaster-Kuratowski-Mazurkiewicz type theorems on covering of the geometric simplex are presented.

MSC:

05B35 Combinatorial aspects of matroids and geometric lattices
47H10 Fixed-point theorems
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
54H25 Fixed-point and coincidence theorems (topological aspects)
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