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 Lindelöf space is normal.

$F_\sigma$ sets 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.

"Lindelöf space" is owned by yark. [ full author list (2) | owner history (1) ]

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Also defines:

Lindelöf, Lindelöf property

Keywords:

topology

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Cross-references: countably compact, images, continuous, compact, subcover, countable, open cover, topological space
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This is version 7 of Lindelöf space, born on 2002-01-04, modified 2007-05-23.
Object id is 1226, canonical name is Lindelof.
Accessed 5263 times total.

Classification:

54D20 (General topology :: Fairly general properties :: Noncompact covering properties )

Pending Errata and Addenda

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