利用 KKM 定理

arXiv - MATH - General Topology Pub Date : 2024-08-07 DOI:arxiv-2408.03921

Daniel McGinnis, Shira Zerbib

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引用次数: 0

摘要

KKM 定理是 Knaster、Kuratowski 和 Mazurkiewicz 于 1929 年提出的，它是定点理论中的一个基本结果，并得到了无数的扩展和应用。在本文中，我们考察了 KKM 定理的新旧概括及其在穿孔数、质量分割、公平除法和匹配理论等领域的应用。我们还给出了一些利用 KKM 型定理的新结果，并讨论了相关的未决问题。

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Using the KKM theorem

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.

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arXiv - MATH - General Topology

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