Characterizing continuous functions on compact, Hasudorff spaces

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

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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 languageEnglish
Pages (from-to)695-728
Number of pages34
JournalAdvances in Mathematics
Issue number2
Publication statusPublished - 10 Nov 2006


  • continuous
  • compactify
  • compact Hausdorff
  • topologize
  • compact metric


Dive into the research topics of 'Characterizing continuous functions on compact, Hasudorff spaces'. Together they form a unique fingerprint.

Cite this