Idzik, Adam; Junosza-Szaniawski, Konstanty Combinatorial lemmas for nonoriented pseudomanifolds. (English) Zbl 1038.05010 Topol. Methods Nonlinear Anal. 22, No. 2, 387-398 (2003). 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) Keywords:Sperner lemma type theorems; pseudomanifolels; primoid; Knaster-Kuratowski-Mazurkiewicz type theorems; geometric simplex PDFBibTeX XMLCite \textit{A. Idzik} and \textit{K. Junosza-Szaniawski}, Topol. Methods Nonlinear Anal. 22, No. 2, 387--398 (2003; Zbl 1038.05010) Full Text: DOI