Using the KKM theorem

Fuente: arXiv
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Main Authors: McGinnis, Daniel, Zerbib, Shira
Format: Preprint
Published: 2024
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author McGinnis, Daniel
Zerbib, Shira
author_facet McGinnis, Daniel
Zerbib, Shira
contents The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this paper we survey old and recent generalizations of the KKM theorem and their applications in the areas of piercing numbers, mass partition, fair division, and matching theory. We also give a few new results utilizing KKM-type theorems, and discuss related open problems.
format Preprint
id arxiv_https___arxiv_org_abs_2408_03921
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Using the KKM theorem
McGinnis, Daniel
Zerbib, Shira
Combinatorics
General Topology
55M20, 52A35, 05C70, 91B50
The KKM theorem, due to Knaster, Kuratowski, and Mazurkiewicz in 1929, is a fundamental result in fixed-point theory, which has seen numerous extensions and applications. In this paper we survey old and recent generalizations of the KKM theorem and their applications in the areas of piercing numbers, mass partition, fair division, and matching theory. We also give a few new results utilizing KKM-type theorems, and discuss related open problems.
title Using the KKM theorem
topic Combinatorics
General Topology
55M20, 52A35, 05C70, 91B50
url https://arxiv.org/abs/2408.03921