## Discretely star-Lindelöf spaces.(English)Zbl 1011.54020

A space $$X$$ is called (discretely) star-Lindelöf if for every open cover $$\mathcal U$$ of $$X$$ there exists a (discrete closed) countable subset $$B$$ of $$X$$ such that $$St(B,{\mathcal U})=X$$. In this paper the relationships between these spaces and $$\omega_1$$-compact spaces are investigated, and some basic properties for example hereditary properties, mapping properties and product properties of discretely star-Lindelöf spaces are obtained.

### MSC:

 54D20 Noncompact covering properties (paracompact, Lindelöf, etc.) 54B05 Subspaces in general topology 54B10 Product spaces in general topology

### Keywords:

discretely star-Lindelöf; $$\omega_1$$-compact
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