ThmDex – An index of mathematical definitions, results, and conjectures.
Result R1176 on D529: Map inverse image
Inverse image of a constant map is either empty or equal to the domain set
Formulation 2
Let $f : X \to Y$ be a D1519: Constant map from $X$ to $Y$ such that
(i) $B \subseteq Y$ is a D78: Subset of $Y$
Then \begin{equation} f^{-1}(B) \in \{ \emptyset, X \} \end{equation}