- Results in Nonlinear Analysis
- Volume:3 Issue:1
- KKM implies the Brouwer fixed point theorem: Another proof
KKM implies the Brouwer fixed point theorem: Another proof
Authors : Sehie PARK
Pages : 12-17
View : 41 | Download : 24
Publication Date : 2020-03-31
Article Type : Research Paper
Abstract :It is well-known that the Brouwer fixed point theorem insert ignore into journalissuearticles values(BFPT);, the weak Sperner combinatorial lemma, and the Knaster-Kuratowski-Mazurkiewicz insert ignore into journalissuearticles values(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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