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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 $$\kappa$$.

##### MSC:
 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 54B10 Product spaces in general topology 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)
##### Keywords:
separable; CCC; countably compact; embedding; box product