Editing Function (mathematics) (section)

== Function space ==
{{Main|Function space|Functional analysis}}
In [[mathematical analysis]], and more specifically in [[functional analysis]], a '''function space''' is a set of [[scalar-valued function|scalar-valued]] or [[vector-valued function]]s, which share a specific property and form a [[topological vector space]]. For example, the real [[smooth function]]s with a [[compact support]] (that is, they are zero outside some [[compact set]]) form a function space that is at the basis of the theory of [[distribution (mathematics)|distributions]].

Function spaces play a fundamental role in advanced mathematical analysis, by allowing the use of their algebraic and [[topology|topological]] properties for studying properties of functions. For example, all theorems of existence and uniqueness of solutions of [[ordinary differential equation|ordinary]] or [[partial differential equation]]s result of the study of function spaces.