Rational Number Space is Topological Space/Proof 1

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

Proof
From Rational Numbers form Metric Space we have that $\Q$ is a metric space under the Euclidean metric.

From Metric Induces Topology, it follows that the Euclidean topology forms a topology on $\Q$.