Definition:Choice Function/Chosen Element

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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 $S$.

Also see

  • Results about choice functions can be found here.