Projectively regular (T2, T1) weakly developable semitopological groups

Abstract

In this paper, we introduce the notion of weakly ω-balanced semitopological groups and prove that the class of weakly ω-balanced semitopological groups is closed under taking subgroups and products. It is prove that a regular (Hausdorff, $T_1$) semitopological group G admits a homeomorphic embedding as a subgroup into a product of regular (Hausdorff, $T_1$) semitopological groups with a weak development if and only if G is weakly ω-balanced and $Ir\left(G\right)\le \omega$ ($Hs\left(G\right)\le \omega$, $Sm\left(G\right)\le \omega$).