Let \(p\colon X\to Y\) be a surjective map. A subset \(U\subseteq X\) is saturated with respect to \(p\) if for every \(y\in Y\) with \(U\cap \inverseof{p}(y)\neq\emptyset\) we have \(\inverseof{p}(y)\subseteq U\).
A subset \(U\subseteq X\) is saturated with respect to \(p\) if and only if \(U = \inverseof{p}(B)\) for some \(B\subseteq Y\), in which case \(B = p(U)\).
See [@Mun00].