A Note on Quasi-Lindelof Spaces

The quasi-Lindel"of property was first introduced by Arhangelski in \cite{Arc}, as a strengthening of the weakly Lindel"of property. However, unlike Lindel"of and weakly Lindel"of spaces, very little is known about how quasi-Lindel"of 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-Lindel"of spaces. We consider several examples: a weakly Lindel"of space which is not quasi-Lindel"of, a product of Lindel"of spaces which is not even quasi-Lindel"of, and a quasi-Lindel"of space which is not ccc. At the end, we pose some open questions.