Lindelöf space
Type of topological space / From Wikipedia, the free encyclopedia
In mathematics, a Lindelöf space[1][2] 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[3] is a topological space such that every subspace of it is Lindelöf. Such a space is sometimes called strongly Lindelöf, but confusingly that terminology is sometimes used with an altogether different meaning.[4] The term hereditarily Lindelöf is more common and unambiguous.
Lindelöf spaces are named after the Finnish mathematician Ernst Leonard Lindelöf.