# Function Space

(redirected from*Space of function*)

## function space

[′fəŋk·shən ‚spās] (mathematics)

A metric space whose elements are functions.

## Function Space

a set of functions for which there is defined a notion of distance or, more generally, of proximity between any two functions. A function space is called linear if, along with any two elements *f _{1}* and

*f*it contains all their linear combinations αf

_{2}_{1}, + βf

_{2}, where α and β are real or complex numbers. An example of a linear function space is the space

*C(a, b*) of all continuous functions on the interval

*[a, b]*with the distance p(

*f*) between two functions being given by the formula

_{1}, f_{2}Function spaces are the most important concrete linear spaces studied in functional analysis. [28–388–1 ]