Definition:Preimage/Mapping/Subclass
< Definition:Preimage | Mapping(Redirected from Definition:Preimage of Subclass under Mapping)
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Definition
Let $V$ be a basic universe.
Let $A \subseteq V$ and $B \subseteq V$ be classes.
Let $f: A \to B$ be a class mapping.
Let $D \subseteq B$.
The preimage of $D$ under $f$ is defined as:
- $f^{-1} \sqbrk D = \set {x \in A: \map f x \in D}$
That is, it is the class of all $x$ such that $\tuple {x, y} \in f$ for $y \in D$.
Also see
- Results about preimages can be found here.