Definition:Left-Total Relation/Multifunction

Definition
In the field of complex analysis, a left-total relation is usually referred to as a multifunction.

A multifunction may not actually be a mapping at all, as (by implication) there may exist elements in the domain which are mapped to more than one element in the codomain.

However, if $\mathcal R$ is regarded as a function from $S$ to the power set of $T$, then left-totality of the relation is the same as totality of this lifted function.

See the definition of an induced mapping.

Also known as
A multifunction is also known as a many-valued function, a multiple-valued function or a multi-valued function.

On the terse form multifunction is preferred.