On M-separability of countable spaces and function spaces
Copyright policy )On M-separability of countable spaces and function spaces
We study M-separability as well as some other combinatorial versions of separability. In particular, we show that the set-theoretic hypothesis b=d implies that the class of selectively separable spaces is not closed under finite products, even for the spaces of continuous functions with the topology of pointwise convergence. We also show that there exists no maximal M-separable countable space in the model of Frankiewicz, Shelah, and Zbierski in which all closed P-subspaces of w^* admit an uncountable family of nonempty open mutually disjoint subsets. This answers several questions of Bella, Bonanzinga, Matveev, and Tkachuk.
Comment: 7 pages
- University of Vienna Austria
- University of Ljubljana Slovenia
Selection principles, 1010 Mathematics, Primary: 54D20, Secondary: 54D65, 1010 Mathematik, Separability of topological spaces, Menger property, Selection principle, M-separable space, Maximal space, Cardinality properties (cardinal functions and inequalities, discrete subsets), M-separability, Geometry and Topology, Mathematics - General Topology
Selection principles, 1010 Mathematics, Primary: 54D20, Secondary: 54D65, 1010 Mathematik, Separability of topological spaces, Menger property, Selection principle, M-separable space, Maximal space, Cardinality properties (cardinal functions and inequalities, discrete subsets), M-separability, Geometry and Topology, Mathematics - General Topology
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