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 or perfectly separable space.

Some sources render this without the hyphen: second-countable.

Also see

 * Countability Axioms