Subgroups of products of Nagata semitopological groups and related results

Abstract

In this article, we introduce notions which are called property (c*) and property (M ₃*) for semitopological groups. We show that if G is a regular semitopological group with a q-point, property (c*) and Sm(G) ≤ ω, 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 the third part of this article, we give an internal characterization of subgroups of product of firstcountable M ₁-semitopological groups. 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*).