# Functions with compact support A [function](Analysis%20(index)#Functions), $f$ is said to have compact support if its _[Support](Support.md)_ is a [Compact](Compact.md) set. This would mean that $f=0$ outside of the compact set. ## Examples of functions with and without compact support * A [function](analysis%20(index)#Functions) that _does not_ have compact support is $f(x)=x^2$ since its domain $f:\mathbb{R}\rightarrow\mathbb{R}^+$ (all positive real numbers) is a set that does not have [[Compact support]]. * a [[bump function]] is an example of a function with compact support. #MathematicalFoundations/Analysis #MathematicalFoundations/Geometry/Topology