Definition:Image (Relation Theory)/Mapping/Mapping/Class Theory

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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.