Cantor Space is Perfect

Theorem
Let $T = \struct {\CC, \tau_d}$ be the Cantor space.

Then $\CC$ is a perfect set of the real number space $\R$ under the usual (Euclidean) topology $\tau_d$.

Proof
From Cantor Space is Dense-in-itself, $\CC$ contains no isolated points.

We also have that the Cantor Set is Closed in Real Number Space.

The result follows from the definition of perfect set.