A Note on Quasi-Lindelof Spaces

Abstract

The quasi-Lindelöf property was first introduced by Arhangelski in \cite{Arc}, as a strengthening of the weakly Lindelöf property. However, unlike Lindelöf and weakly Lindelöf spaces, very little is known about how quasi-Lindelöf spaces behave under the main topological operations, and how the property relates to separation axioms. In the present paper, we look at several properties of quasi-Lindelöf spaces. We consider several examples: a weakly Lindelöf space which is not quasi-Lindelöf, a product of Lindelöf spaces which is not even quasi-Lindelöf, and a quasi-Lindelöf space which is not ccc. At the end, we pose some open questions.

Proceedings of the 41st Spring Conference of the Union of Bulgarian Mathematicians (2012)