Topological semigroups from quasi-pseudometrics and quasi-norms: an asymmetric generalization [Articol]

Abstract

We explore topologies on semigroups and groups induced by families of quasipseudometrics and quasi-norms, aiming to transform them into topological semigroups and groups. We establish conditions under which these topologies are compatible with the algebraic operations of semigroups and groups. Finally, we demonstrate the potential of these topologies to endow a group into a bitopological group structure.