Cantor Space is Second-Countable

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 a second-countable space.

Proof
We have that the Cantor set is a topological subspace of the real number space $\R$.

We also have that the Real Number Space is Second-Countable.

The result follows from Second-Countability is Hereditary.