# Definition:Cantor Space

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## Definition

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**.

## Also known as

For ease of notation, usually one simply writes $\tau_d$ instead of $\tau_\CC$.

## 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.