Expansive homeomorphisms on quasi-metric spaces

Abstract

The investigation of expansive homeomorphisms in metric spaces began with Utz in 1950. Thereafter, several authors have extensively stud-ied this concept for different motivations. In this current article, we study expansive homeomorphism in the context of quasi-pseudometric spaces. This is motivated by the fact that any expansive homeomor-phism on quasi-pseudometric space is again expansive homeomorphism on its induced pseudometric space but the converse is not true in general. Moreover, the study of orbit structures has been taken to con-sideration in this article. For instance, we investigate the denseness oforbits in the context of quasi-metric spaces.