Rational Number Space is Second-Countable

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 second-countable.

Proof
From Rational Numbers form Metric Space, $\left({\Q, \tau_d}\right)$ is a metric space.

From Rational Number Space is Separable, $\left({\Q, \tau_d}\right)$ is a separable space.

The result follows from Separable Metric Space is Second-Countable.