\begin{definition}[Definition:Left-Total Relation/Multifunction/Branch]
Let $D \subseteq \C$ be a subset of the complex numbers.
Let $f: D \to \C$ be a multifunction on $D$.
Let $\family {S_i}_{i \mathop \in I}$ be a partitioning of the codomain of $f$ such that:
:$\forall i \in I: f \restriction_{D \times S_i}$ is a mapping.
Then each $f \restriction_{D \times S_i}$ is a '''branch''' of $f$.
\end{definition}