Definition:Image (Relation Theory)/Mapping/Mapping/Class Theory
< Definition:Image (Relation Theory) | Mapping | Mapping(Redirected from Definition:Image of Mapping (Class Theory))
Jump to navigation
Jump to search
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.
The image of $\RR$ is defined and denoted as:
- $\Img \RR := \set {y \in V: \exists x \in V: \tuple {x, y} \in \RR}$
That is, it is the class of all $y$ such that $\tuple {x, y} \in \RR$ for at least one $x$.
Also known as
Some sources refer to this as the direct image of a mapping, in order to differentiate it from an inverse image.
Rather than apply a mapping $f$ directly to a subset $A$, those sources often prefer to define the direct image mapping of $f$ as a separate concept in its own right.
In the context of set theory, the term image set of mapping for $\Img f$ can often be seen.
Also see
- Results about images can be found here.