On \(\mathcal L\)-starcompact spaces. (English) Zbl 1164.54356

Summary: A space \(X\) is \(\mathcal L\)-starcompact if for every open cover \(\mathcal U\) of \(X\), there exists a Lindelöf subset \(L\) of \(X\) such that \(\text{St} (L,{\mathcal U})=X.\) We clarify the relations between \(\mathcal L\)-starcompact spaces and other related spaces and investigate topological properties of \(\mathcal L\)-starcompact spaces.


54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
54B10 Product spaces in general topology
54D55 Sequential spaces
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