A generalization of M-separability by networks

Maddalena Bonanzinga, Davide Giacopello


All spaces are assumed to be Tychonoff. A space is M-separable if for every sequence (Dn : n ∈ ω) of dense subsets of X one can pick finite FnDn, such that ⋃ n ∈ ωFn is dense in X. Every space having a countable base is M-separable but not every space with countable network weight is M-separable. We introduce a new Menger type property defined by networks, called M-nw-selective property, such that every M-nw-selective space has countable network weight and is M-separable. By analogy, we also introduce H- and R- nw-selective spaces for Hurewicz and Rothberger type properties. Several properties of the new classes of spaces are studied and some questions are posed. ⊂


Countable network weight; M-separable space, H-separable space, R-separable space, Menger space, Hurewicz space, Rothberger space.

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DOI: https://doi.org/10.1478/AAPP.1012A11

Copyright (c) 2023 Maddalena Bonanzinga, Davide Giacopello

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