Constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions by Sperner's lemma

TL;DR

This paper provides a constructive proof of Brouwer's fixed point theorem for a specific class of functions using Sperner's lemma, advancing the understanding of fixed point existence in a constructive framework.

Contribution

It introduces a new constructive proof of Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions using Sperner's lemma.

Findings

Constructive proof of Brouwer's fixed point theorem for the specified functions

Application of Sperner's lemma to a modified partition of a simplex

Advancement in constructive fixed point theory

Abstract

In this paper using Sperner's lemma for modified partition of a simplex we will constructively prove Brouwer's fixed point theorem for sequentially locally non-constant and uniformly sequentially continuous functions.