In this article, we give an internal characterization of subgroups of products of semitopological groups which satisfy certain properties that imply D-property. For example, we give an internal characterization of subgroups of products of regular semitopological groups which satisfy open (G), give an internal characterization of subgroups of products of regular first-countable semitopological groups which satisfy property (sigma-A) (property (sigma-B)). Every first-countable semitopological group with Collins-Roscoe property satisfies pre-(G) and property (pre-sigma-B). We finally show that if G is a Hausdorff countably compact semitopological group with Hs(G) <= omega and G satisfies property (pre-sigma-B) (pre-(G)), then G is a topological group. (C) 2022 Elsevier B.V. All rights reserved.
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