Subgroups of products of Nagata semitopological groups and related results (Q6622104)

The author introduces notions of property \((c*)\) and property \((M_{3}*)\) for semitopological groups. He shows that if \(G\) is a regular semitopological group with a \(q\)-point, property \((c*)\) and \(Sm(G) \leq \omega\), then \(G\) is topologically isomorphic to a subgroup of the product of a family of first-countable \(M_1\)-semitopological groups (Nagata semitopological groups). In addition, the author gives an internal characterization of subgroups of products of first countable \(M_1\)-semitopological groups. That is, a semitopological (paratopological) group \(G\) is topologically isomorphic to a subgroup of the product of a family of first-countable \(M_1\)-semitopological (paratopological) groups if and only if \(G\) satisfies the \(T_0\) separation axiom and has property \((M_{3}*)\).