# standard n-ball

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

Canonical name | StandardNball |

Date of creation | 2013-03-22 16:52:49 |

Last modified on | 2013-03-22 16:52:49 |

Owner | Mathprof (13753) |

Last modified by | Mathprof (13753) |

Numerical id | 6 |

Author | Mathprof (13753) |

Entry type | Definition |

Classification | msc 55M99 |

Synonym | unit n-ball |

Synonym | unit ball |

Synonym | standard $n$-ball |

Defines | n-cell |