Fiber

Definition

Let $q:X\to Y$ be any map. A subset of the form $q^{-1}(y)$ for $y\in Y$ is called a fiber of $q$. A subset $U\subseteq X$ is called saturated with respect to $q$, if $U=q^{-1}(V)$ for some $V\subseteq Y$ $U$ is then a collection of fibers.