\begin{definition}[Definition:Disk]
Consider the Euclidean space $\left({\R^n, d}\right)$, where $d$ is the Euclidean metric.
An '''open $n$ dimensional disk''' (or '''ball''') is defined as:
:$\mathbb D^n = \left\{{x \in \R^n : d \left({x, y}\right) < r}\right\}$
where $y \in \R^n$ is called the '''center''' and $r \in \R_+$ is called the '''radius'''.
A '''closed $n$-disk''' is defined as:
:$\mathbb D^n = \left\{{x \in \R^n : d \left({x, y}\right) \le r }\right\}$
{{wtd|Add the definition as it applies specifically to the complex numbers $\C$.}}
{{refactor|put the below somewhere else}}
The boundary of $\mathbb D^n$ is denoted $\partial \mathbb D^n$, and is $\mathbb S^{n-1}$, the $(n-1)$-sphere.
\end{definition}