Map (mathematics)

A map is a function, as in the association of any of the four colored shapes in X to its color in Y

In mathematics, a map or mapping is a function in its general sense.[1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.[2]

The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial.[3][4] In category theory, a map may refer to a morphism.[2] The term transformation can be used interchangeably,[2] but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.

  1. ^ The words map, mapping, correspondence, and operator are often used synonymously. Halmos 1970, p. 30. Some authors use the term function with a more restricted meaning, namely as a map that is restricted to apply to numbers only.
  2. ^ a b c "Mapping | mathematics". Encyclopedia Britannica. Retrieved 2019-12-06.
  3. ^ Apostol, T. M. (1981). Mathematical Analysis. Addison-Wesley. p. 35. ISBN 0-201-00288-4.
  4. ^ Stacho, Juraj (October 31, 2007). "Function, one-to-one, onto" (PDF). cs.toronto.edu. Retrieved 2019-12-06.