## On $$\mathcal K$$-starcompact spaces.(English)Zbl 1134.54314

Summary: A space $$X$$ is $$\mathcal K$$-starcompact if for every open cover $$\mathcal U$$ of $$X$$, there exists a compact subset $$K$$ of $$X$$ such that $$St(K,{\mathcal U})=X$$, where $$St(K,{\mathcal U})=\bigcup\{U\in{\mathcal U}: U\cap K\neq\emptyset\}$$. In this paper, we investigate the relations between $$\mathcal K$$-starcompact spaces and other related spaces. We also study topological properties of $$\mathcal K$$-starcompact spaces.

### MSC:

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

### Keywords:

countably compact; star-compact; $$1\frac12$$-star compact
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