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