Page "Kakutani fixed-point theorem" Paragraph 5

; Set-valued function: A set-valued function φ from the set X to the set Y is some rule that associates one or more points in Y with each point in X.

Formally it can be seen just as an ordinary function from X to the power set of Y, written as φ: X → 2 < sup > Y </ sup >.

Some prefer the term correspondence, which is used to refer to a function that for each input may return many outputs.

Thus, each element of the domain corresponds to a subset of one or more elements of the range.