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arXiv · 0804.3199

Computable counter-examples to the Brouwer fixed-point theorem

Petrus H. Potgieter
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Abstract

This paper is an overview of results that show the Brouwer fixed-point theorem (BFPT) to be essentially non-constructive and non-computable. The main results, the counter-examples of Orevkov and Baigger, imply that there is no procedure for finding the fixed point in general by giving an example of a computable function which does not fix any computable point. Research in reverse mathematics has shown the BFPT to be equivalent to the weak König lemma in RCA$_0$ (the system of recursive comprehension) and this result is illustrated by relating the weak König lemma directly to the Baigger example.

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Petrus H. Potgieter. 2008-04-21. Computable counter-examples to the Brouwer fixed-point theorem. https://arxiv.org/abs/0804.3199

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