vanish at infinity
Let be a locally compact space. A function is said to vanish at infinity if, for every , there is a compact set such that for every , where denotes the standard norm (http://planetmath.org/Norm2) on .
The set of continuous functions that vanish at infinity is an algebra over the complex field and is usually denoted by .
When is compact, all functions vanish at infinity. Hence, .
|Title||vanish at infinity|
|Date of creation||2013-03-22 17:50:57|
|Last modified on||2013-03-22 17:50:57|
|Last modified by||asteroid (17536)|
|Synonym||zero at infinity|
|Synonym||vanishes at infinity|