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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