TOPOLOGICAL QUASIGROUPS

Abstract

A semitopological quasigroup is defined and certain conditions are found under which a semitopological quasigroup is a topological quasigroup. Some properties of topological quasigroups are obtained. It is proved that (i) a realvalued continuous function defined on a compact subset of a topological left or right loop satisfying the second axiom of countability is uniformly continuous on it, (ii) a regular left or right Haar measure can be defined in any locally compact Hausdorff quasigroup satisfying certain conditions.