View source for Function space

In [[mathematics]], a '''function space''' is a [[Set (mathematics)|set]] of [[Function (mathematics)|functions]] of a given kind from a set X to a set Y.

== Description ==

It is called a [[Space (mathematics)|space]] because in many applications it is a [[topological space]] (including [[Metric space|metric spaces]]), a [[vector space]], or both.

Namely, if Y is a [[Field (mathematics)|field]], functions have inherent vector structure with two operations of [[pointwise]] addition and multiplication to a scalar.

Topological and metrical structures of function spaces are more diverse.

== See also ==

* [[Clifford algebra]]
* [[Functional determinant]]
* [[List of mathematical functions]]
* [[Spectral theory]]
* [[Tensor field]]

== External links ==

* [https://en.wikipedia.org/wiki/Function_space Function space] @ Wikipedia.org 


[[Category:Functions]]
[[Category:Mathematics]]