Definition:Second-Countable Space

Definition
A topological space $T = \left({S, \tau}\right)$ is second-countable or satisfies the Second Axiom of Countability 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.

aims to be consistent in presentation, and the hyphenated version is preferred.

Also see

 * Definition:Countability Axioms