A function which assigns to each element $x\in X$ a subset $f(x)$ of a set $Y$: $f(x)\subset Y$, where there is at least one such subset of $Y$ consisting of at least two elements. See also Multi-valued mapping.
Multi-valued function. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Multi-valued_function&oldid=31981