Computability in Europe 2006
Logical Approaches to Computational Barriers

Regular Talk:
Computable counter-examples to the Brouwer fixed-point theorem

Speaker: Petrus H. Potgieter
Slot: Array, 12:00-12:20, col. 1


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 shows 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.

websites: Arnold Beckmann 2008-06-11