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13.
On the Menger covering property and ▫$D$▫-spaces
Repovš, Dušan, 1954- ; Zdomskyy, Lyubomyr, 1983-
The main results of this paper are: (1) It is consistent that every subparacompact space ▫$X$▫ of size ▫$\omega_1$▫ is a ▫$D$▫-space; (2) If there exists a Michael space, then all productively ...Lindelöf spaces have the Menger property and, therefore, are ▫$D$▫-spaces; (3) Every locally ▫$D$▫-space which admits a ▫$\sigma$▫-locally finite cover by Lindelöf spaces is a ▫$D$▫-space.
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