and related technical fields, the term map
is often a synonym
. Thus, for example, a partial map
is a partial function
, and a total map
is a total function
. Related terms like domain
, etc. can be applied equally to maps and functions, with the same meaning.
In many branches of mathematics, the term is qualified with a property specific to that branch, such as a continuous function in topology, a linear map in linear algebra, etc.
Some authors such as Serge Lang use map as a general term for an association of an element in the range with every element in the domain, and function only to refer to maps in which the range is a field.
Sets of maps with special properties are the subjects of many important theories: see for instance Lie group, mapping class group, permutation group.
In formal logic, the term is sometimes used for a functional predicate, whereas a function is a model of such a predicate in set theory.
In graph theory, a map is a drawing of a graph on a surface without intersecting edges (a planar graph).
In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems. See also Poincaré map.