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

Yasuhito Tanaka

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arXiv · 1103.1776

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

Yasuhito Tanaka

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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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BibTeX RIS

Yasuhito Tanaka. 2011-08-23. Constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant functions. https://arxiv.org/abs/1103.1776

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