On M-separability of countable spaces and function spaces |
| |
Authors: | Dušan Repovš Lyubomyr Zdomskyy |
| |
Institution: | a Faculty of Mathematics and Physics, and Faculty of Education, University of Ljubljana, P.O. Box 2964, Ljubljana, Slovenia 1001 b Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Straße 25, A-1090 Wien, Austria |
| |
Abstract: | 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 ω* admit an uncountable family of nonempty open mutually disjoint subsets. This answers several questions of Bella, Bonanzinga, Matveev, and Tkachuk. |
| |
Keywords: | M-separable space Menger property Selection principles Maximal space |
本文献已被 ScienceDirect 等数据库收录! |
|