\begin{definition}[Definition:Cantor Space]
Let $\CC$ be the Cantor set.
Let $\tau_d$ be the Euclidean topology on $\R$.
Then since $\CC \subseteq \R$, we can endow $\CC$ with the subspace topology $\tau_\CC$.
The topological space $\struct {\CC, \tau_\CC}$ is referred to as the '''Cantor space'''.
\end{definition}