KKM implies the Brouwer fixed point theorem: Another proof


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Authors

  • Sehie Park

Keywords:

Abstract convex space; KKM space; Brouwer fixed point theorem; Sperner lemma, metric type space.

Abstract

It is well-known that the Brouwer fixed point theorem (BFPT), the weak Sperner combinatorial lemma, and the Knaster-Kuratowski-Mazurkiewicz (KKM) theorem are mutually equivalent and have scores of equivalent formulations and several thousand applications. It is well-known that KKM deduced the BFPT from Sperner Lemma. In this article, we recall some KKM theoretic results implying the BFPT.

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Published

2022-11-07

How to Cite

Sehie Park. (2022). KKM implies the Brouwer fixed point theorem: Another proof. Results in Nonlinear Analysis, 3(1), 12–17. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/41