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Characterizing continuous functions on compact spaces |
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| Authors: | C Good S Greenwood RW Knight |
| Institution: | a School of Mathematics and Statistics, University of Birmingham, Birmingham, B15 2TT, UK b Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand c Worcester College, Walton Street, Oxford, OX1 2HB, UK d Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, Canada |
| Abstract: | We consider the following problem: given a set X and a function  , 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. |
| Keywords: | primary 54A10 54B99 54C05 54D30 54H20 |
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