On the Menger covering property and $D$-spaces

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 Lindelöf spaces have the Menger property, and, therefore, are $D$-spaces; and Every locally $D$-space which admits a $\sigma$-locally finite cover by Lindelöf spaces is a $D$-space.

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

References in corpus (3)

• A semifilter approach to selection principles
• Set-theoretic problems concerning Lindelof spaces
• Productively Lindelof spaces may all be D

Cited by in corpus (6)

• Topological games and Alster spaces
• Selective covering properties of product spaces
• Lindelof spaces which are indestructible, productive, or D
• Set-theoretic problems concerning Lindelof spaces
• Productively Lindelöf spaces and the covering property of Hurewicz
• Definable versions of Menger's conjecture