standard n-ball

The standard n-ball is Bn={xn|||x||1}, where ||x||2=i=1nxi2. 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 Vn , Dn ,En or E¯n.

The boundary of the standard n-ball is Sn-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