Dense subgroups of paratopological groups

We show that if H   is a dense subgroup of a T3T3 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 T3T3 and it contains a dense topological subgroup.We show that the functors T3T3 and Reg(G)Reg(G) do not respect dense subgroups of semitopological groups. This answers a problem posed by Mikhail Tkachenko.