Rational Number Space is Meager

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 of the first category.

Proof
From Rational Numbers are Countably Infinite, $\Q$ is the union of singleton subsets.

From Singleton Set is Nowhere Dense in Rational Space, each of those singleton subsets is nowhere dense in $\left({\Q, \tau_d}\right)$.

The result follows from definition of first category.