On ωS-balanced semitopological groups

Abstract

In this paper we introduce the notion of ωs-balanced semitopological groups. We show that a regular (Hausdorff, T1) semitopological group G admits a homeomorphic embedding as a subgroup into a product of regular (Hausdorff, T1) semitopological groups with a strong development if and only if G is ωs-balanced and Ir(G) ≤ ω (Hs(G) ≤ ω, Sm(G) ≤ ω).  We also characterize first-countable ωs-balanced semitopological group in terms of strong development.