Lindelöf space


A topological spaceMathworldPlanetmath is said to be Lindelöf if every open cover has a countableMathworldPlanetmath subcover.


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

A regularPlanetmathPlanetmathPlanetmathPlanetmath ( Lindelöf space is

Fσ sets ( in Lindelöf spaces are Lindelöf. ContinuousPlanetmathPlanetmath images of Lindelöf spaces are Lindelöf.

A Lindelöf space is compactPlanetmathPlanetmath 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 SeparablePlanetmathPlanetmath
Related topic Compact
Related topic LindelofTheorem
Related topic CompactMetricSpacesAreSecondCountable
Related topic ErnstLindelof
Defines Lindelöf
Defines Lindelöf property