R-factorizable groups and subgroups of Lindelِf P-groups

The main subject of our study are P-groups, that is, the topological groups whose Gδ-sets are open. We establish several elementary properties of P-groups and then prove that a P-group is R-factorizable iff it is pseudo-ω1-compact iff it is ω-stable. This characterization is used to show that direct products of R-factorizable P-groups as well as continuous homomorphic images of R-factorizable P-groups are R-factorizable. A special emphasis is placed on the study of subgroups of Lindelöf P-groups. ncept of stability is applied to prove that if G is a dense subgroup of a direct product of Lindelöf Σ-groups, then every continuous homomorphic image of G is R-factorizable and perfectly κ-normal.