Remainders in compactifications of semitopological and paratopological groups (Q471486)

In this paper, the authors mainly discuss the remainders of semitopological and paratopological groups. The authors show that if the Hausdorff compactification \(bG\) of a non-locally compact semitopological \(G\) has a remainder with a locally a point-countable base, then \(bG\) is separable and metrizable, which gives a positive answer to a question posed in [\textit{H. Wang} and \textit{W. He}, Topology Appl. 164, 14--23 (2014; Zbl 1283.54018)]. Moreover, the authors discuss the remainders in the class of non-locally compact \(\mathbb{R}_1\)-factorizable paratopological groups, and answer some questions in the paper [\textit{F. Lin, C. Liu} and \textit{L. H. Xie}, Ukr. Math. J. 66, No. 4, 561--571 (2014) and Ukr. Mat. Zh. 66, No. 4, 500--509 (2014; Zbl 1311.22004)].