Definition:Disk

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Complex disk

Let $a \in \C$ be a complex number.

Let $R>0$ be a real number.

Open disk

The open (complex) disk of center $a$ and radius $R$ is the set:

$B(a, R) = \{z\in \C : |z-a| < R\}$

where $|\cdot|$ denotes complex modulus.

Closed disk

The closed (complex) disk of center $a$ and radius $R$ is the set:

$B(a, R) = \{z\in \C : |z-a| \leq R\}$

where $|\cdot|$ denotes complex modulus.

Euclidean disk

Let $n\geq 1$ be a natural number.

Let $\left({\R^n, d}\right)$ be the $n$-dimensional Euclidean space, where $d$ is the Euclidean metric.

Let $a\in \R^n$.

Let $r>0$ be a real number.

Open disk

The open $n$-disk of center $a$ and radius $r$ is the set:

$\mathbb D^n(a, r) = \left\{{x \in \R^n : d \left({x, a}\right) < r}\right\}$

Closed disk

A closed $n$-disk of center $a$ and radius $r$ is the set:

$\overline {\mathbb D}^n(a, r) = \left\{{x \in \R^n : d \left({x, a}\right) \le r }\right\}$

The boundary of $\mathbb D^n$ is denoted $\partial \mathbb D^n$, and is $\mathbb S^{n-1}$, the $(n-1)$-sphere.

Internationalization

Disk is translated:

 In Dutch: schijf (literally: disk)