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17th "Summer" Conference on Topology and Applications
July 1-4, 2002
University of Auckland
Auckland, New Zealand

Organizers
David Gauld (University of Auckland), Sina Greenwood (University of Auckland), David McIntyre (University of Auckland), Warren Moors (Waikato University), Sidney Morris (University of South Australia), Vladimir Pestov (Victoria University Wellington), Ivan Reilly (University of Auckland), Des Robbie (University of Melbourne)

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Compactifying functions
by
David McIntyre
University of Auckland
Coauthors: Chris Good (Birmingham University), Sina Greenwood (University of Auckland), Robin Knight (Oxford University), Stephen Watson (York University)

We consider the following problem: given a set X and a function T:X --> X, does there exist a compact Hausdorff topology on X which makes T continuous? We give a necessary and sufficient for such a topology to exist, subject to the assumption that T has at least one fixed point, and generalise this to a condition concerning the divisors of the lengths of the cycles under T. We also show that if T has no fixed points or cycles and X has cardinality less than \mathfrakc then there is no such topology.

Date received: June 28, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-67.