# Definition:Lindelöf Space

## Definition

A topological space $T = \struct {S, \tau}$ is a Lindelöf space if and only if every open cover of $S$ has a countable subcover.

## Also see

Some sources classify this as a countability property.

Other sources treat it as a compactness property.

• Results about Lindelöf spaces can be found here.

## Source of Name

This entry was named for Ernst Leonard Lindelöf.