# Lindelöf space

## Definition

A topological space is said to be Lindelöf if every open cover has a countable subcover.

## Notes

A second-countable space is Lindelöf. A compact space is Lindelöf.

A regular (http://planetmath.org/T3Space) Lindelöf space is http://planetmath.org/node/1530normal.

$F_{\sigma}$ sets (http://planetmath.org/F_sigmaSet) in Lindelöf spaces are Lindelöf. Continuous images of Lindelöf spaces are Lindelöf.

A Lindelöf space is compact if and only if it is countably compact.

 Title Lindelöf space Canonical name LindelofSpace Date of creation 2013-03-22 12:06:34 Last modified on 2013-03-22 12:06:34 Owner yark (2760) Last modified by yark (2760) Numerical id 11 Author yark (2760) Entry type Definition Classification msc 54D20 Related topic SecondCountable Related topic Separable Related topic Compact Related topic LindelofTheorem Related topic CompactMetricSpacesAreSecondCountable Related topic ErnstLindelof Defines Lindelöf Defines Lindelöf property