## 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

### Keywords:

compact space; countably compact space; Lindelöf space
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