Characterization of ℝ-factorizable G-spaces

Abstract

The ℝ-factorizability of G-spaces is characterized in the paper and the equivalence of ℝ-factorizability and ω-U property is proved for G-spaces with d-open actions of ω-narrow groups. It is shown that the ℝ-factorizability characterizes those compact coset spaces which are coset spaces of ω-narrow groups. The concepts of m- and M-factorizable G-spaces are introduced, which generalizes the corresponding concepts for topological groups.