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