Rational Number Space is Separable

Theorem
Let $\struct {\Q, \tau_d}$ be the rational number space under the Euclidean topology $\tau_d$.

Then $\struct {\Q, \tau_d}$ 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.