Primary
Mapping ○꠹｜Definition｜1st｜20260107012219-00-⌔
Map (mathematics)
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.34 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.
Printed 2026-06-28.
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Link to original Footnotes
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. ↩
“Mapping (mathematics)”. Encyclopedia Britannica. Retrieved 2019-12-06. ↩ ↩2 ↩3
Apostol, T. M. (1981). Mathematical Analysis. Addison-Wesley. p. 35. ISBN 0-201-00288-4. ↩
Stacho, Juraj (October 31, 2007). “Function, one-to-one, onto” (PDF). cs.toronto.edu. Retrieved 2019-12-06. ↩
Secondary
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