\begin{definition}[Definition:Left-Total Relation/Multifunction]
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 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 a direct image mapping.
{{explain|"lifted function"}}
\end{definition}