- In mathematics and related technical fields, a
**mapping**or**map**is a variation on the theme of a function. - Most commonly, the terms are simply synonyms for
*function*. Along these lines, a*partial mapping*is a*partial function*, and a*total mapping*is a*total function*. - In many specific branches of mathematics, the term is used for a function with a standard property relevant to that branch, such as a
*continuous function*in topology, a*linear transformation*in linear algebra, etc. In Wikipedia, we always include a relevant adjective like "continuous" or "smooth" to avoid confusion. - In formal logic, the term "mapping" is sometimes used for a
*functional predicate*, whereas a function is a model of such a predicate in set theory. - In computer science, a mapping is the relationship between a key and its value in an associative array.
- In cognitive psychology, a mapping is the relationship between a source domain and target domain, typically reflecting a conceptual metaphor.