# Category:Cantor Space

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This category contains results about the Cantor space.

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**.

## Subcategories

This category has only the following subcategory.

### C

## Pages in category "Cantor Space"

The following 15 pages are in this category, out of 15 total.

### C

- Cantor Space as Countably Infinite Product
- Cantor Space is Compact
- Cantor Space is Complete Metric Space
- Cantor Space is Dense-in-itself
- Cantor Space is Meager in Closed Unit Interval
- Cantor Space is Non-Meager in Itself
- Cantor Space is not Extremally Disconnected
- Cantor Space is not Locally Connected
- Cantor Space is not Scattered
- Cantor Space is Nowhere Dense
- Cantor Space is Perfect
- Cantor Space is Second-Countable
- Cantor Space is Totally Separated
- Cantor Space satisfies all Separation Axioms