MAP (MATHEMATICS)

In mathematics and related technical fields, the term 'map' or 'mapping' is often a synonym for ''function''; see function (mathematics). Thus, for example, a ''partial map'' is a ''partial function'', and a ''total map'' is a ''total function''. Related terms like ''domain'', ''codomain'', ''injective'', ''continuous'', etc. can be applied equally to maps and functions, with the same meaning.
In many branches of mathematics, the term denotes a function with a property specific to that branch, such as a ''continuous function'' in topology, a ''linear map'' in linear algebra, etc.
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.
In the theory of dynamical systems, a map denotes an evolution function used to create discrete dynamical systems.

Contents

See also

See also

★ Bijection, injection and surjection

★ Category theory

★ Function

★ Homeomorphism

★ Homomorphism

★ Mapping class group

★ Morphism

★ Topology