Completions of paratopological groups and bounded sets

Abstract

In this paper we consider two questions in the realm of paratopological groups: When does multiplication on a given Tychonoff paratopological group H admit an extension to continuous multiplication on the Dieudonné completion, μH, of H in such a way that H turns into a dense subgroup of the paratopological group μH? and, if A and B are bounded subsets of paratopological groups G and H, respectively, is A × B bounded in G × H? The motivation for these questions comes from the field of topological groups and they are receiving a special attention as an interesting source of open problems.