⋆-quasi-pseudometrics on algebraic structures.

In this paper, we introduce some concepts of ⋆-(quasi)-pseudometric spaces, and give an example which shows that there is a ⋆-quasipseudometric 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. [ABSTRACT FROM AUTHOR]