Lindelöf space

Summary

A Lindelöf space is a topological space in which every open cover has a countable subcover. It is a weakening of compactness, where finite subcovers are replaced by countable ones. Every second-countable space is Lindelöf, and every regular Lindelöf space is paracompact. For metric spaces, being Lindelöf, separable and second-countable are the same.