Projectively regular \((T_2, T_1)\) weakly developable semitopological groups (Q6611768)

The authors introduce the notion of weakly \(\omega\)-balanced semitopological groups and prove that the class of weakly \(\omega\)-balanced semitopological groups is closed under taking subgroups and products. The authors also show 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 \(\omega\)-balanced and \(Ir(G) \leq \omega\) \((Hs(G) \leq \omega, Sm(G) \leq \omega)\).