Before revision: In mathematical analysis, a multivalued function is a set-valued function that has a further continuity property, namely that the choice of an element in the set defines a corresponding element in each set for close to , and thus defines locally an ordinary function .
After revision: Set-valued functions are also known as multivalued functions in some references, but herein and in many others references in mathematical analysis, a multivalued function is a set-valued function that has a further continuity property, namely that the choice of an element in the set defines a corresponding element in each set for close to , and thus defines locally an ordinary function .