Definition:Disk
Definition
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:
- $\mathbb D^n = \left\{{x \in \R^n : d \left({x, y}\right) \le r }\right\}$
The boundary of $\mathbb D^n$ is denoted $\partial \mathbb D^n$, and is $\mathbb S^{n-1}$, the $(n-1)$-sphere.
Add the definition as it applies specifically to the complex numbers $\C$.
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Note
The open disc of radius $r$ is a particular instance of an $r$-neighborhood in $\left({\R^n, d}\right)$.
