Projectively regular (T2, T1) weakly developable semitopological groups

In this paper, we 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. It is prove that a regular (Hausdorff, T-1) semitopological group C 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 C is weakly omega-balanced and Ir (G) <= w (Hs(G) <= w, Sm (G) <= w). (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.