KKM implies the Brouwer fixed point theorem: Another proof

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

Kaynakça

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