Projectively first-countable semitopological groups with certain \(D\)-properties (Q2673848)

In this paper, the authors give an internal characterization of subgroups of products of semitopological groups which satisfy certain properties that imply the \(D\)-property. For example, they give an internal characterization of subgroups of products of regular semitopological groups which satisfy open (G) and give an internal characterization of subgroups of products of regular first-countable semitopological groups which satisfy property (\(\sigma\)-A) (property (\(\sigma\)-B)). Finally, they show that if \(G\) is a Hausdorff countably compact semitopological group with \(Hs(G)\leq \omega\) and \(G\) satisfies property (pre-\(\sigma\)-B) (pre-(G)), then \(G\) is a topological group.