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On \(\mathcal C\)-starcompact spaces. (English) Zbl 1199.54146

Summary: A space \(X\) is \(\mathcal C\)-starcompact if, for every open cover \(\mathcal U\) of \(X\), there exists a countably compact subset \(C\) of \(X\) such that \(\operatorname {St}(C,{\mathcal U})=X.\) In this paper, we investigate the relations between \(\mathcal C\)-starcompact spaces and other related spaces, and also study topological properties of \(\mathcal C\)-starcompact spaces.

MSC:

54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54D55 Sequential spaces
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