A survey of D-spaces

A space X is a D-space if whenever one is given a neighborhood N (x) of x for each x ∈ X, then there is a closed discrete subset D of X such that {N (x) : x ∈ D} covers X. It is a decades-old open question whether some of the standard covering properties, such as Lindelof or paracompact, imply D. This remains unsettled, yet there has been a considerable amount of interesting recent work on D-spaces. We give a survey of this work.

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