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...
| প্রধান লেখক: | , , , |
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| বিন্যাস: | Journal article |
| প্রকাশিত: |
Elsevier
2006
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| সংক্ষিপ্ত: | <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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