Definition:Cantor Space

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.