Rational Number Space is Completely Normal

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

Then $\struct {\Q, \tau_d}$ is a completely normal space.

Proof
From Euclidean Space is Complete Metric Space, a Euclidean space is a metric space.

From Metric Space fulfils all Separation Axioms it follows that $\struct {\Q, \tau_d}$ is a completely normal space.