On M-separability of countable spaces and function spaces

Details On M-separability of countable spaces and function spaces On M-separability of countable spaces and function spaces

2010-10-12

arxiv.org/abs/1010.2474v1

Topology and its Applications 157 (2010), 2538-2541

Mathematics

General Topology

7 pages

Scientific paper

10.1016/j.topol.2010.07.036

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.

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