Discretely star-Lindelöf spaces (Q1848101)

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.