The MathResource
one-many,
adj. (of a function or mapping) capable of associating a single member of the domain with more than one member of the range of a set-valued function; holding between the same first argument and more than one second argument of a binary relation, as illustrated by the figure below. For example, sin-Ix and √ x are one-many functions on the positive real numbers;... is the mother of... is a one-many relation, since a mother may have many children but every child has exactly one mother.

One-many. A one-many mapping from S to T.