Products of star-Lindelöf and related spaces (Q2747322)

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 \(\kappa\).