Article

Remarks on ω-domination of discrete subspaces

Published in: Quaestiones Mathematicae
Volume 42 , issue 8 , 2019 , pages: 1091–1099

DOI: 10.2989/16073606.2018.1504831

Author(s): Yan-Kui Song Institute of Mathematics, School of Mathematical Science, P.R. China , Wei-Feng Xuan School of Statistics and Mathematics, P.R. China

Keywords: Primary 54D20 , 54A25 , Secondary 54A35 , Primary 54D20 , 54A25 , Secondary 54A35

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Abstract

Given a space X, we will say that a class

of subsets of X is dominated by a class Ɓ if for any A ∈ , there exists a B ∈ Ɓ such that A ⊂ . In particular, all (closed) discrete subsets of X are countably dominated (which we frequently abbreviate as ω-dominated) if, for any (closed) discrete set D ⊂ X, there exists a countable set B ⊂ X such that D ⊂ . In this paper, we investigate the topological properties of spaces in which (closed) discrete subspaces are dominated either by countable subsets or by Lindelöf subspaces.

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