Family of closed convex sets covering faces of a simplex
Horst Kramer, A. B. N\'emeth

TL;DR
This paper explores a convex variant of Sperner's lemma, focusing on covering faces of a simplex with closed convex sets, offering new insights into combinatorial topology.
Contribution
It introduces a novel convex approach to Sperner's lemma, extending classical combinatorial results to convex geometric settings.
Findings
Established conditions for covering faces of a simplex with convex sets
Proved new convex Sperner-type lemmas
Extended combinatorial topology results to convex geometry
Abstract
It is considered a special, convex variant of Sperner lemma type .
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Taxonomy
TopicsPoint processes and geometric inequalities · Mathematics and Applications · Advanced Combinatorial Mathematics
