Definition:Second-Countable Space

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Definition

A topological space $T = \left({S, \tau}\right)$ is second-countable or satisfies the Second Axiom of Countability if and only if its topology has a countable basis.


Also known as

Also known as:

a completely separable space
a perfectly separable space.

Some sources render this without the hyphen: second countable.

$\mathsf{Pr} \infty \mathsf{fWiki}$ aims to be consistent in presentation, and the hyphenated version is preferred.


Also see

  • Results about second-countable spaces can be found here.


Sources