On strongly Lindelöf spaces (Q2703104)

A topological space \(X\) is called strongly Lindelöf if every cover of \(X\) by preopen sets has a countable subcover. This class of spaces has been introduced by the reviewer in 1989. One main result there says that a space is strongly Lindelöf if and only if it is Lindelöf and \(d\)-Lindelöf (i.e. every cover by dense sets has a countable subcover). In the present paper the authors improve this result. Moreover, they introduce several new concepts to obtain additional characterizations of strongly Lindelöf spaces and \(d\)-Lindelöf spaces.