Mapping

Mapping is the creation of maps, a graphic symbolic representation of the significant features of a part of the surface of the Earth.

Map (mathematics)

In mathematics, the term mapping, usually shortened to map, refers to either

There are also a few, less common uses in logic and graph theory.

Maps as functions

In many branches of mathematics, the term map is used to mean a function, sometimes with a specific property of particular importance to that branch. For instance, a "map" is a continuous function in topology, a linear transformation in linear algebra, etc.

Some authors, such as Serge Lang, use "function" only to refer to maps in which the codomain is a set of numbers, i.e., a subset of the fields R or C, and the term mapping for more general functions.

Sets of maps of special kinds are the subjects of many important theories: see for instance Lie group, mapping class group, permutation group.

In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. See also Poincaré map.