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Products of star-Lindelöf and related spaces. (English) Zbl 0983.54006
A space \(X\) is called star-Lindelöf if for every open cover \({\mathcal U}\) of \(X\), the cover \(\{St(x,{\mathcal U}):x\in X\}\) has a countable subcover. Lindelöf, countably compact and separable spaces are star-Lindelöf. The authors survey and generalize some known results on star-Lindelöf spaces. They also consider a number of related properties such as centered-Lindelöf, \(\sigma\)-centered-Lindelöf and linked-Lindelöf. We mention one new result: for a regular space \(X\), the product \(X^\kappa\) is star-Lindelöf for every cardinal \(\kappa\) if and only if \(X^\kappa\) is countably compact for every cardinal \(\kappa\).

54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
54B10 Product spaces in general topology
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)