Characterizing continuous functions on compact, Hasudorff spaces

Christopher Good; S Greenwood; R Knight; D MacIntyre; D Watson

doi:10.1016/j.aim.2005.11.002

Characterizing continuous functions on compact, Hasudorff spaces

Christopher Good, S Greenwood, R Knight, D MacIntyre, D Watson

Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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 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. (C) 2005 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	695-728
Number of pages	34
Journal	Advances in Mathematics
Volume	206
Issue number	2
DOIs	https://doi.org/10.1016/j.aim.2005.11.002
Publication status	Published - 10 Nov 2006

Keywords

continuous
compactify
compact Hausdorff
topologize
compact metric

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10.1016/j.aim.2005.11.002

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KW - topologize

KW - compact metric

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Characterizing continuous functions on compact, Hasudorff spaces

Abstract

Keywords

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