Constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant functions

2011/03/09 by Yasuhito Tanaka, Tanaka, Yasuhito
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1103.1776

arxiv created 2011/08/23 · arxiv updated 2011/08/24

Abstract

We present a constructive proof of Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions based on the existence of approximate fixed points. And we will show that Brouwer's fixed point theorem for uniformly continuous and sequentially locally non-constant functions implies Sperner's lemma for a simplex. Since the existence of approximate fixed points is derived from Sperner's lemma, our Brouwer's fixed point theorem is equivalent to Sperner's lemma.

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