# 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**

- Results about
**the Cantor space**can be found here.

## Source of Name

This entry was named for Georg Cantor.