Sehie PARK

KKM implies the Brouwer fixed point theorem: Another proof

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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Başlangıç: 2018
Yayıncı: Erdal KARAPINAR

Arşiv

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