function space

Set of functions of a given kind from a set X to a set Y; it is called a space because in many applications it is a topological space (including metric spaces), a vector space, or both

EntityQ934367

Subclass of: space
, exponential object

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited by the function space. For example, the set of functions from any set X into a vector space has a natural vector space structure given by pointwise addition and scalar multiplication. In other scenarios, the function space might inherit a topological or metric structure, hence the name function space. Often in mathematical jargon, especially in analysis or geometry, a function could refer to a map of the form or where is the space in question. Whilst other maps of the form between any two spaces are simply referred to as maps. Example of this can be the space of compactly supported functions on a topological space. However in a larger context a function space could just consist of a set of functions equipped with possibly some extra structure.

Overview

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21 statements · 24% with external sources · numbers in brackets are citations

Characteristic of: function

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18 identifiers linking function space across the web's reference databases

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statements

24%

externally sourced

Source last edited June 12, 2026. AIDB refreshes this page daily.

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AIDB. (2026). function space (Q934367). Retrieved from https://aidb.si/e/function-space-Q934367