extension of a function

Let f:XY be a function and A and B be sets such that XA and YB. An extensionPlanetmathPlanetmath of f to A is a function g:AB such that f(x)=g(x) for all xX. Alternatively, g is an extension of f to A if f is the restrictionPlanetmathPlanetmath of g to X.

Typically, functions are not arbitrarily extended. Rather, it is usually insisted upon that extensions have certain properties. Examples include analytic continuations and meromorphic extensions.

Title extension of a function
Canonical name ExtensionOfAFunction
Date of creation 2013-03-22 17:51:00
Last modified on 2013-03-22 17:51:00
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 6
Author Wkbj79 (1863)
Entry type Definition
Classification msc 03E20
Related topic RestrictionOfAFunction
Defines extension