On the Menger covering property and $D$-spaces

Details On the Menger covering property and $D$-spaces On the Menger covering property and $D$-spaces

2010-12-06

arxiv.org/abs/1012.1094v1

Proc. Amer. Math. Soc. 140 (2012), 1069-1074

Mathematics

General Topology

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

Scientific paper

10.1090/S0002-9939-2011-10945-6

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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