Set-valued function

For multi-valued functions of mathematical analysis, see Multivalued function. For functions whose arguments are sets, see Set function.

This diagram represents a multi-valued, but not a proper (single-valued) function, because the element 3 in X is associated with two elements, b and c, in Y.

A set-valued function, also called a correspondence or set-valued relation, is a mathematical function that maps elements from one set, the domain of the function, to subsets of another set. Set-valued functions are used in a variety of mathematical fields, including optimization, control theory and game theory.

Set-valued functions are also known as multivalued functions in some references, but this article and the article Multivalued function follow the authors who make a distinction.