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 ${\overline{E}}^{n}$.

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 called an n-cell.

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

Title standard n-ball StandardNball 2013-03-22 16:52:49 2013-03-22 16:52:49 Mathprof (13753) Mathprof (13753) 6 Mathprof (13753) Definition msc 55M99 unit n-ball unit ball standard $n$-ball n-cell