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Discretely star-Lindelöf spaces. (English) Zbl 1011.54020

A space \(X\) is called (discretely) star-Lindelöf if for every open cover \(\mathcal U\) of \(X\) there exists a (discrete closed) countable subset \(B\) of \(X\) such that \(St(B,{\mathcal U})=X\). In this paper the relationships between these spaces and \(\omega_1\)-compact spaces are investigated, and some basic properties for example hereditary properties, mapping properties and product properties of discretely star-Lindelöf spaces are obtained.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B05 Subspaces in general topology
54B10 Product spaces in general topology
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