partial mapping

Let X1,,Xn and Y be sets, and let f be a function of n variables: f:X1×X2××XnY. xiXi for 2in. The induced mapping af(a,x2,,xn) is called the partial mapping determined by f corresponding to the first variable.

In the case where n=2, the map defined by af(a,x) is often denoted f(,x). Further, any function f:X1×X2Y determines a mapping from X1 into the set of mappings of X2 into Y, namely f¯:x(yf(x,y)). The converseMathworldPlanetmath holds too, and it is customary to identify f with f¯. Many of the “canonical isomorphisms” that we come across (e.g. in multilinear algebra) are illustrations of this kind of identification.

Title partial mapping
Canonical name PartialMapping
Date of creation 2013-03-22 13:59:31
Last modified on 2013-03-22 13:59:31
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 03E20