On strong cellularity type properties of Lindelof groups

Abstract

We prove several facts about cellularity and κ-cellularity of λ-Lindelöf groups generated by their κ-stable subspaces. For example, if a Lindelöf group G is generated by its κ-stable subspace then κ-cellularity (and hence cellularity) of G does not exceed κ. In particular, ω1-cellularity (and hence cellularity) of a Lindelöf group does not exceed ω1 if this group is generated by its ω1-Lindelöf subspace which is a P-space. For any cardinal μ with ω<μ c a Lindelöf group G is constructed which is separable (and hence has countable cellularity) while ω-cellularity of G is equal to μ.