ThmDex – An index of mathematical definitions, results, and conjectures.
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▼ Zermelo-Fraenkel set theory
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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}
Also known as
Map preimage
Children
▶ D2947: Level set
Results
▶ R4534
▶ R4756
▶ R4538: Inclusion of image does not imply inclusion of inverse image
▶ R4755: Inverse image of a reflected real set
▶ R4470: Inverse image of countable union is union of inverse images
▶ R352: Inverse image of image
▶ R2074: Isotonicity of inverse image