Characterising continuous functions on compact spaces.
<p>We consider the following problem: given a set <em>X</em> and a function <em>T : X andrightarrow; X</em>, does there exist a compact Hausdorff topology on <em>X</em> which makes <em>T</em> continuous? We characterize such functions in terms of...
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| Fformat: | Journal article |
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Elsevier
2006
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| Crynodeb: | <p>We consider the following problem: given a set <em>X</em> and a function <em>T : X andrightarrow; X</em>, does there exist a compact Hausdorff topology on <em>X</em> which makes <em>T</em> 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.</p> |
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