Rational Number Space is Topological Space/Proof 1

Theorem
The set $\Q$ of rational numbers under the Euclidean topology $\tau$ 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 $\Q$.