Cantor Space is Second-Countable

Theorem
Let $T = \left({\mathcal C, \tau_d}\right)$ be the Cantor space.

Then $T$ is a second-countable space.

Proof
We have that the Cantor space 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.