Constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant functions
Logic
2011-08-24 v2
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.
Cite
@article{arxiv.1103.1776,
title = {Constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant functions},
author = {Yasuhito Tanaka},
journal= {arXiv preprint arXiv:1103.1776},
year = {2011}
}