关于一致空间的扩张同胚

Pub Date : 2021-12-01 DOI:10.2478/ausm-2021-0018

A. Barzanouni, E. Shah

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引用次数: 0

摘要

摘要研究一致空间上的扩张同胚的概念。证明了如果在一致空间上存在拓扑可扩张的同胚，则该空间始终是Hausdor空间，因此是正则空间。进一步，我们用拓扑可扩同胚来刻画轨道可扩同胚，并得出如果紧致一致空间上存在拓扑可扩同胚，则该空间总是可度量的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On expansive homeomorphism of uniform spaces

Abstract We study the notion of expansive homeomorphisms on uniform spaces. It is shown that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a Hausdor space and hence a regular space. Further, we characterize orbit expansive homeomorphisms in terms of topologically expansive homeomorphisms and conclude that if there exist a topologically expansive homeomorphism on a compact uniform space then the space is always metrizable.

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