Let  
$X,Y$ sets,  
$X_1\subseteq X$,  
$Y_1\subseteq Y$,  
$F=\mathcal{P}(X\times Y)$ the set of all functions in $X\times Y$,  
$f=\{\tilde{f}\in F\ |\ \forall x((x\in\text{dom}(\tilde{f}))\land (x\in X_1)) \colon \tilde{f}(x)\in Y_1\}$.