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arXiv · 1012.1094

On the Menger covering property and $D$-spaces

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.

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BibTeXRIS

Dušan Repovš, Lyubomyr Zdomskyy. 2010-12-06. On the Menger covering property and $D$-spaces. https://doi.org/10.1090/s0002-9939-2011-10945-6

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