Functional

A mapping \$f\$ of an arbitrary set \$X\$ into the set \$\mathbb R\$ of real numbers or the set \$\mathbb C\$ of complex numbers. If \$X\$ is endowed with the structure of a vector space, a topological space or an ordered set, then there arise the important classes of linear, continuous and monotone functionals, respectively (cf. Linear functional; Continuous functional; Monotone mapping).

References

 [1] A.N. Kolmogorov, S.V. Fomin, "Elements of the theory of functions and functional analysis" , 1–2 , Graylock (1957–1961) (Translated from Russian)
How to Cite This Entry:
Functional. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Functional&oldid=29314
This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article