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

Yasuhito Tanaka

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arXiv · 1105.3616

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

Yasuhito Tanaka

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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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BibTeX RIS

Yasuhito Tanaka. 2011-05-18. Constructive proofs of Tychonoff's and Schauder's fixed point theorems for sequentially locally non-constant functions. https://arxiv.org/abs/1105.3616

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