On strong cellularity type properties of Lindelöf groups |
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Authors: | D. Buhagiar B. Pasynkov |
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Affiliation: | a Department of Mathematics, University of Malta, Msida MSD.06, Malta b General Topology and Geometry, Mechanics and Mathematics Faculty, Moscow State University, 119899 Moscow, Russia |
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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. |
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Keywords: | 54H11 54A25 54B35 54D20 |
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