# Definition:Second-Countable Space

## Definition

A topological space $T = \struct {S, \tau}$ 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.