Discretely star-Lindelöf spaces. (English) Zbl 1011.54020

Song, Yan-Kui

Tsukuba J. Math. 25, No. 2, 371-382 (2001).

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.

Reviewer: Shou Lin (Ningde, Fujian)

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