A note on semitopological groups and paratopological groups

We give a description of the T2T2-reflection of a semitopological group G as the quotient of G with respect to a certain subgroup of G. This answers an open problem of M. Tkachenko (Problem 4.1 which appears in [6]). We also show that if G is an ω-cellular regular ω-balanced paratopological group then the following conditions are equivalent:(1)Sm(G)≤ωSm(G)≤ω;(2)Hs(G)≤ωHs(G)≤ω;(3)Ir(G)≤ωIr(G)≤ω.