Difference between revisions of "Functional"
From Encyclopedia of Mathematics
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| − | A [[Mapping|mapping]] | + | {{TEX|done}} |
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| + | A [[Mapping|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|vector space]], a [[Topological space|topological space]] or an [[Ordered set|ordered set]], then there arise the important classes of linear, continuous and monotone functionals, respectively (cf. [[Linear functional|Linear functional]]; [[Continuous functional|Continuous functional]]; [[Monotone mapping|Monotone mapping]]). | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.N. Kolmogorov, S.V. Fomin, "Elements of the theory of functions and functional analysis" , '''1–2''' , Graylock (1957–1961) (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.N. Kolmogorov, S.V. Fomin, "Elements of the theory of functions and functional analysis" , '''1–2''' , Graylock (1957–1961) (Translated from Russian)</TD></TR></table> | ||
Latest revision as of 06:47, 16 January 2013
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
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