Constructive proofs of Tychonoff's and Schauder's fixed point theorems for sequentially locally non-constant functions

2011/05/18 by Yasuhito Tanaka, Tanaka, Yasuhito
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.1105.3616

arxiv created 2011/05/18 · arxiv updated 2011/05/19

Abstract

We present a constructive proof of Tychonoff's fixed point theorem in a locally convex space for sequentially locally non-constant functions, As a corollary to this theorem we also present Schauder's fixed point theorem in a Banach space for sequentially locally non-constant functions. We follow the Bishop style constructive mathematics.

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