\begin{definition}[Definition:Left-Total Relation/Multifunction/Branch/Principal Branch]
Let $D \subseteq \C$ be a subset of the complex numbers.
Let $f: D \to \C$ be a multifunction on $D$.
Let $\sequence {S_i}_{i \mathop \in I}$ be a partitioning of the codomain of $f$ into branches.
It is usual to distinguish one such branch of $f$ from the others, and label it the '''principal branch''' of $f$.
\end{definition}