In mathematics, a Lindelöf space is a topological space in which every open cover has a countable subcover. The Lindelöf property is a weakening of the more commonly used notion of compactness, which requires the existence of a finite subcover.

A strongly Lindelöf space is a topological space such that every open subspace is Lindelöf. Such spaces are also known as hereditarily Lindelöf spaces, because all subspaces of such a space are Lindelöf.