Subgroups of products of semitopological groups with a strong development

Abstract

Using the notion of ωs-balanced semitopological group and some cardinal invariants, Kumar and Tyagi [7] characterize when a regular (T1, Hausdorff) semitopological group admits a homeomorphic embedding as a subgroup into a product of regular (T1, Hausdorff)  semitopological groups with a strong development. In this paper, we show that a T0 semitopological group G is topologically isomorphic to a subgroup of a topological product of T0 semitopological groups with a strong development if and only if G is ωs-balanced. Then the  main theorems of [7] are immediate consequences of our result mentioned above.