Editing Bump function (section)

{{Short description|Smooth and compactly supported function}}
[[File:Bump.png|thumb|350x350px|The graph of the bump function <math>(x, y) \in \Reals^2 \mapsto \Psi(r),</math> where <math>r = \left(x^2 + y^2\right)^{1/2}</math> and <math>\Psi(r) = e^{-1/(1 - r^2)} \cdot \mathbf{1}_{\{|r|<1\}}.</math>]]
In [[mathematical analysis]], a '''bump function''' (also called a '''test function''') is a [[Function (mathematics)|function]] <math>f : \Reals^n \to \Reals</math> on a [[Euclidean space]] <math>\Reals^n</math> which is both [[smooth function|smooth]] (in the sense of having [[Continuous function|continuous]] [[derivative]]s of all orders) and [[Support (mathematics)#Compact support|compactly supported]].  The [[Set (mathematics)|set]] of all bump functions with [[Domain of a function|domain]] <math>\Reals^n</math> forms a [[vector space]], denoted <math>\mathrm{C}^\infty_0(\Reals^n)</math> or <math>\mathrm{C}^\infty_\mathrm{c}(\Reals^n).</math>  The [[dual space]] of this space endowed with a suitable [[Topological space#Definitions|topology]] is the space of [[Distribution (mathematics)|distributions]].