choice function

Let \(X_i\) be sets for \(i \in I\) and \(X \coloneqq \bigcup_{i \in I} X_i\) be the union. Then a choice function is a map

\begin{align*} f: I \rightarrow& X \\ i \mapsto& x_i \end{align*}

with \(x_i \in X_i\)