★-quasi-pseudometrics on algebraic structures

Abstract

In this paper, we introduce some concepts of ★-(quasi)-pseudometric spaces, and give an example which shows that there is a ★-quasi-pseudometric space which is not a quasi-pseudometric space. We also study the conditions under which ★-quasi-pseudometric semitopological groups are paratopological groups or topological groups.

Keywords

• invariant ★-(quasi-)pseudometric
• topological group
• paratopological groups
• topological semigroup