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Homesecond countable

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# second countable

*second countable* if it has a countable basis.
It can be shown that a second countable space is both Lindelöf and separable, although the converses fail. For instance, the lower limit topology on the real line is both Lindelöf and separable, but not second countable.

Related:

Separable, Lindelof, EverySecondCountableSpaceIsSeparable, LindelofTheorem, UrysohnMetrizationTheorem, FirstAxiomOfCountability, LocallyCompactGroupoids, FirstCountable

Synonym:

second axiom of countability, completely separable, perfectly separable, second-countable

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

54D70*no label found*

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