Rational Number Space is Separable

Theorem
Let $\left({\Q, \tau_d}\right)$ be the rational number space under the Euclidean topology $\tau_d$.

Then $\left({\Q, \tau_d}\right)$ is separable.

Proof
From Rational Numbers are Countably Infinite, $\Q$ is itself countable.

The result follows from Underlying Set of Topological Space is Everywhere Dense.