Odd-Even Topology is Separable

Theorem
Let $T = \left({\Z_{>0}, \tau}\right)$ be a topological space where $\tau$ is the odd-even topology on the strictly positive integers $\Z_{>0}$.

Then $T$ is separable.

Proof
From Odd-Even Topology is Second-Countable, $T$ is second-countable.

The result follows from Second-Countable Space is Separable.