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Homestandard n-ball

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# standard n-ball

The *standard n-ball* is $B^{n}=\{x\in\mathbb{R}^{n}|\quad||x||\leq 1\}$,
where $||x||^{2}=\sum_{{i=1}}^{n}{x_{i}}^{2}$.
The standard n-ball is also called the *unit n-ball* or the
*n-disk*.

The notation in the literature for the standard n-ball is not uniform. Sometimes it is denoted by $V^{n}$ , $D^{n}$ ,$E^{n}$ or ${\overline{E}}^{n}$.

A space that is homeomorphic to the standard n-ball is called
an *n-cell*.

A 1-cell is called an arc and a 2-cell is called a disk.

Defines:

n-cell

Synonym:

unit n-ball, unit ball, standard $n$-ball

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

55M99*no label found*

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