Category:Definitions/Choice Functions

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This category contains definitions related to Choice Functions.
Related results can be found in Category:Choice Functions.

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.

A choice function on $\mathbb S$ is a mapping $f: \mathbb S \to \ds \bigcup \mathbb S$ satisfying:

$\forall S \in \mathbb S: \map f S \in S$

That is, for a given set in $\mathbb S$, a choice function selects an element from that set.