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.

Keywords

• expansive homeomorphism
• orbit expansive homeomorphism
• uniform spaces
• primary 37b99, 37c50
• secondary 54h20