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.