Remainders in compactifications of semitopological and paratopological groups

In this paper, the remainders of semitopological and paratopological groups are investigated. We mainly establish that if G is a non-locally compact semitopological group and bG is a compactification of G such that Y=bG∖G has locally a point-countable base, then bG is separable and metrizable. This gives a positive answer to a question posed in Wang and He (2014) [25]. We also show that if G is a non-locally compact R1-factorizable paratopological group and Y=bG∖G is a local ℵ-space, then bG is separable and metrizable. Some questions in [14] are answered.