Definition:Choice Function/Chosen Element

Definition
Let $\mathbb S$ be a set of sets such that:
 * $\forall S \in \mathbb S: S \ne \O$

that is, none of the sets in $\mathbb S$ may be empty.

Let $f: \mathbb S \to \ds \bigcup \mathbb S$ be a choice function on $\mathbb S$.

For a given $S \in \mathbb S$, the image $\map f S$ of $S$ is referred to as the $f$-chosen element of $S$.