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On spaces which are linearly D. (English) Zbl 1180.54009

Summary: We introduce a generalization of D-spaces, which we call linearly D-spaces. The following results are obtained for a T 1 -space X.

X is linearly Lindelöf if, and only if, X is a linearly D-space of countable extent.

X is linearly D provided that X is submetaLindelöf.

X is linearly D provided that X is the union of finitely many linearly D-subspaces.

X is compact provided that X is countably compact and X is the union of countably many linearly D-subspaces.

MSC:
54A25Cardinality properties of topological spaces
54D20Noncompact covering properties (paracompact, Lindelöf, etc.)
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