Quasi-boundedness of irresolute paratopological groups

Abstract Continuing the study of irresolute paratopological groups, our focus in this paper is to define and study the boundedness for irresolute paratopological groups. Premeager property for irresolute paratopological groups is discussed. It is proved that every open subgroup of a quasi-bounded, premeager irresolute paratopological group is premeager. For bounded homomorphisms on an irresolute paratopological group, new notions -quasi bounded and -quasi bounded homomorphisms are introduced and discussed.