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Locally \(D\)-spaces. (Chinese. English summary) Zbl 1224.54060

Summary: Different from the case of \(D\)-spaces, the union of a locally finite family of closed locally \(D\)-spaces is still a locally \(D\)-space. It is proved that a perfect mapping preserves the locally \(D\)-space property.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54A05 Topological spaces and generalizations (closure spaces, etc.)
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54E45 Compact (locally compact) metric spaces
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