C-extensions of topological groups

Abstract

We show that if a topological group G is dense and C-embedded in a regular Lindelöf space X then, under mild restrictions on G or X, the space X is a topological group containing G as a dense topological subgroup, and both groups G and X are R-factorizable. This fact includes as a special case the description of pseudocompact topological groups as dense C-embedded subgroups of compact groups obtained by Comfort and Ross in 1966.We also introduce the new notions of (simply) sm-factorizable and densely sm-factorizable topological groups, and establish several relations between these classes of groups on the one hand and the class of R-factorizable groups on the other.