In "mathematics, the term mapping, usually shortened to map, refers to either a "function, often with some sort of special structure, or a "morphism in category theory, which generalizes the idea of a function. There are also a few, less common uses in logic and graph theory.
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.
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. All these usages can be applied to "maps" as general functions or as functions with special properties.
In the communities surrounding "programming languages that treat functions as "first-class citizens, a "map often refers to the "binary "higher-order function that takes a function f and a "list [v0, v1, ..., vn] as "arguments and returns [f(v0), f(v1), ..., f(vn)], where n ≥ 0.