Remainders in compactifications of semitopological and paratopological groups

摘要

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). We also show that if G is a non-locally compact R_1-factorizable paratopological group and Y = bG G is a local N-space, then bG is separable and metrizable. Some questions in are answered.