Hereditarily R-factorizable groups

Mikhail Tkachenko
2010 Topology and its Applications  
MSC: We show that every subgroup of the σ -product of a family {G i : i ∈ I} of regular paratopological groups satisfying Nag(G i ) ω has countable cellularity, is perfectly κnormal and R 3 -factorizable. For topological groups, we prove a more general result as follows. Let C be the minimal class of topological groups that contains all Lindelöf Σgroups and is closed under taking arbitrary subgroups, countable products, continuous homomorphic images, and forming σ -products. Then every group in
more » ... C has countable cellularity, is hereditarily R-factorizable and perfectly κ-normal.
doi:10.1016/j.topol.2008.12.045 fatcat:mckqr6kogrf6naouqvhm26y7sm