We consider the following problem: given a set X and a function T : X andrightarrow; X, does there exist a compact Hausdorff topology on X which makes T continuous? We characterize such functions in terms of their orbit structure. Given the generality of the problem, the characterization turns out to be surprisingly simple and elegant. Amongst other results, we also characterize homeomorphisms on compact metric spaces.
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- Peer review status:
- Peer reviewed
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- Elsevier B.V.
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- Copyright 2005 Elsevier B.V. All rights reserved. Re-use of this article is permitted in accordance with the Terms and Conditions set out at http://www.elsevier.com/open-access/userlicense/1.0/ (accessed 19/02/2014).
Characterising continuous functions on compact spaces.
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