The Brouwer fixed-point theorem is essentially non-constructive since the counter-examples of Orevkov and Baigger imply that there is no general procedure for finding the fixed point – by constructing a computable function which does not fix any (Turing) computable point in the unit square. A new computable enumeration property is proposed which guarantees that whenever a computable function has only non-computable fixed points, a set with this property always contains either none or infinitely many of the fixed points. The counter-examples of Orevkov and Baigger as well as the relation of the problem with the König lemma will be briefly discussed as well.
Pure Maths Seminar
Department of Decision Sciences, University of South Africa
Tue, 17/07/2012 - 12:00pm to 1:00pm
RC-4082, Red Centre Building, UNSW