standard n-ball

The standard n-ball is $B^n=\{x\in {ℝ}^n|\mathit{\hspace{1em}}||x||\le 1\}$,where ${||x||}^2={\sum }_{i=1}^{n}x_i{}^2$.The standard n-ball is also called the unit n-ball or then-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 ${\overline{E}}^n$.

The boundary of the standard n-ball is $S^{n-1}$, the n-1-sphere.

A space that is homeomorphic to the standard n-ball is calledan n-cell.

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