ThmDex – An index of mathematical definitions, results, and conjectures.
Result R30 on D529: Map inverse image
Inverse image of intersection is intersection of inverse images
Formulation 1
Let $f : X \to Y$ be a D18: Map such that
(i) $B_j \subseteq Y$ is a D78: Subset of $Y$ for each $j \in J$
Then \begin{equation} f^{-1} \left( \bigcap_{j \in J} B_j \right) = \bigcap_{j \in J} f^{-1}(B_j) \end{equation}