On the Menger covering property and 𝐷-spaces

Repovš, Dušan; Zdomskyy, Lyubomyr

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

On the Menger covering property and $D$-spaces
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Proc. Amer. Math. Soc. 140 (2012), 1069-1074 Request permission

Abstract:

The main results of this paper 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 Lindelöf spaces have the Menger property and, therefore, are $D$-spaces.

Every locally $D$-space which admits a $\sigma$-locally finite cover by Lindelöf spaces is a $D$-space.

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