p-Boundedness in paratopological groups

Abstract

We show that bounded subsets of ω-admissible paratopological groups are p -bounded for all p∈ω⁎p∈ω⁎. In other words, they have a similar behavior to bounded subsets of topological groups. We present several new classes of ω-admissible paratopological groups. In particular, Hausdorff ω-balanced paratopological groups with countable Hausdorff number belong to this class. Also, we prove that if G is an ω-admissible paratopological group then so is every subgroup of G and its semiregularization. We analyze, by means of the case of locally feebly compact paratopological groups, how the fact that the semiregularization of a paratopological group G is a topological group influences the properties of the bounded subsets of G. Some properties of C-compact subsets of ω-admissible (respectively, locally feebly compact) Hausdorff paratopological groups are studied and some clarifying examples are presented.