<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

On expansive homeomorphism of uniform spaces

Department of Mathematics, School of Mathematical Sciences

Department of Mathematics, Faculty of Science

Acta Universitatis Sapientiae, Mathematica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"On expansive homeomorphism of uniform spaces"}

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,...

On expansive homeomorphism of uniform spaces

Published Online: Dec 30, 2021

Page range: 292 - 304

DOI: https://doi.org/10.2478/ausm-2021-0018

Keywords
expansive homeomorphism, orbit expansive homeomorphism, uniform spaces

© 2021 Ali Barzanouni et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On expansive homeomorphism of uniform spaces

Published Online: Dec 30, 2021

Page range: 292 - 304

DOI: https://doi.org/10.2478/ausm-2021-0018

Keywordsexpansive homeomorphism, orbit expansive homeomorphism, uniform spaces

© 2021 Ali Barzanouni et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
expansive homeomorphism, orbit expansive homeomorphism, uniform spaces