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Characterising continuous functions on compact spaces.

Abstract:

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.

Publication status:
Published
Peer review status:
Peer reviewed
Version:
Publisher's version

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Publisher copy:
10.1016/j.aim.2005.11.002

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
D. W. McIntyre More by this author
S. Greenwood More by this author
Publisher:
Elsevier B.V. Publisher's website
Journal:
Advances in Mathematics Journal website
Volume:
206
Issue:
2
Pages:
695-728
Publication date:
2006-11-05
DOI:
ISSN:
0001-8708
URN:
uuid:2051dd99-1caf-4e29-b2d5-65574b0a23e9
Source identifiers:
28120
Local pid:
pubs:28120

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