Lindelöf space

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 hereditarily Lindelöf space is a topological space of which every subspace is Lindelöf. Such a space is sometimes called strongly Lindelöf, but that terminology is given a different meaning by some authors. The term hereditarily Lindelöf is more common and unambiguous.

Lindelöf spaces are named after the Finnish mathematician Ernst Leonard Lindelöf.