Computable counter-examples to the Brouwer fixed-point theorem
| dc.creator | Potgieter, Petrus H. | |
| dc.date | 2008-04-21 | |
| dc.date.accessioned | 2026-07-07T09:33:43Z | |
| dc.date.available | 2026-07-07T09:33:43Z | |
| dc.description | 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. | |
| dc.description | 10 pages; to appear in local proceedings of Computability in Europe 2008: Logic and Theory of Algorithms | |
| dc.identifier | https://arxiv.org/abs/0804.3199 | |
| dc.identifier | http://arxiv.org/abs/0804.3199 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159229 | |
| dc.subject | General Mathematics | |
| dc.subject | 68Q25; 03D10; 68W99 | |
| dc.title | Computable counter-examples to the Brouwer fixed-point theorem | |
| dc.type | text |