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 $\RR$ is regarded as a mapping from $S$ to the power set of $T$, then left-totality of $\RR$ is the same as totality of this lifted function.

See the definition of a direct image mapping.