In
mathematics,
mapping (or just
map) is a common
synonym for
function. The
traditional definition: a
mapping from a
set X to a
set Y is a
subset f of the
cartesian product X x Y such that, for each element
x of X, there is exactly one y in Y with (x,y) in f. Then this y is denoted f(x), the
value of the
mapping f at x.
If the objects X and Y are more sophisticated structures than sets, for instance topological spaces,
algebras or manifolds, use of the word mapping frequently, but not always, connotes that f preserves the relevant structure. Thus a mapping of topological spaces is a continuous function, a mapping of smooth manifolds is a smooth function, a mapping of groups or algebras is a homomorphism.