Definition:Cantor Space

Definition
Let $\mathcal C$ be the Cantor set.

Let $\tau_d$ be the Euclidean topology on $\R$.

Then since $\mathcal C \subseteq \R$, we can endow $\mathcal C$ with the subspace topology $\tau_{\mathcal C}$.

The topological space $\left({\mathcal C, \tau_{\mathcal C}}\right)$ is referred to as the Cantor space.

Also known as
For ease of notation, usually one simply writes $\tau_d$ instead of $\tau_{\mathcal C}$.

Also see

 * Cantor Set, the underlying set of the Cantor space