Rational Number Space is Topological Space/Proof 2

Theorem
The rational number space $\left({\Q, \tau_d}\right)$ of rational numbers under the Euclidean topology $\tau_d$ forms a topology.

Proof
The real Euclidean space $\left({\R, \tau_d}\right)$ is a topology.

By definition of rational numbers, $\Q \subseteq \R$.

From Topological Subspace is Topological Space we have that $\left({\Q, \tau_d}\right)$ is a topology.