Pre-Image Preserves Intersection
Pre-Image Preserves Intersection
For \(f : X \to Y\) and \(B_i \subseteq Y\) for all \(i \in I\)
\[ f^{-1}\left(\bigcap_{i \in I} B_{i}\right) = \bigcap_{i \in I} f^{-1}(B_{i})\]