Function Space

function space

[′fəŋk·shən ‚spās]

(mathematics)

A metric space whose elements are functions.

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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 f₁ and f₂ it contains all their linear combinations αf₁, + βf₂, 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(f₁, f₂) between two functions being given by the formula

Function spaces are the most important concrete linear spaces studied in functional analysis. [28–388–1 ]

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.