On the Menger covering property and $D$-spaces

Dušan Repovš; Lyubomyr Zdomskyy

doi:10.1090/S0002-9939-2011-10945-6

On the Menger covering property and $D$-spaces

General Topology 2011-12-06 v1 Logic

Authors: Dušan Repovš , Lyubomyr Zdomskyy

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Abstract

The main results of this note are: It is consistent that every subparacompact space $X$ of size $\omega_1$ is a $D$ -space; If there exists a Michael space, then all productively Lindel\"of spaces have the Menger property, and, therefore, are $D$ -spaces; and Every locally $D$ -space which admits a $\sigma$ -locally finite cover by Lindel\"of spaces is a $D$ -space.

Keywords

general topology topological spaces topological properties

Cite

@article{arxiv.1012.1094,
  title  = {On the Menger covering property and $D$-spaces},
  author = {Dušan Repovš and Lyubomyr Zdomskyy},
  journal= {arXiv preprint arXiv:1012.1094},
  year   = {2011}
}

Comments

7 pages, to appear in Proc. Amer. Math. Soc

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