Cantor Space is Non-Meager in Itself

Theorem
Let $\left({\mathcal C, \tau_d}\right)$ be the Cantor set considered as a topological subspace of the real number space $\R$ under the Euclidean topology $\tau_d$.

Then $\mathcal C$ is non-meager in itself.

Proof
We have that the Cantor set is a complete metric space.