KKM implies the Brouwer fixed point theorem: Another proof

Year 2020, Volume: 3 Issue: 1, 12 - 17, 31.03.2020

Sehie Park

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.

Keywords

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

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