Dense subgroups of paratopological groups

We show that if H is a dense subgroup of a T-3 semitopological group G such that H is a paratopological group, then G is a paratopological group as well. Also, we prove that a semitopological group G is a topological group provided G is T-3 and it contains a dense topological subgroup. We show that the functors T-3 and Reg(G) do not respect dense subgroups of semitopological groups. This answers a problem posed by Mikhail Tkachenko. (C) 2015 Elsevier B.V. All rights reserved.