ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Definition D529
Map inverse image
Formulation 0
Let $f : X \to Y$ be a D18: Map.
The inverse image of $E \subseteq Y$ with respect to $f$ is the D11: Set \begin{equation} f^{-1}(E) : = \{ x \in X : f(x) \in E \} \end{equation}
Children
Level set
Results
R4534
R4756
Inclusion of image does not imply inclusion of inverse image
Inverse image of a reflected real set
Inverse image of countable union is union of inverse images
Inverse image of image
Isotonicity of inverse image