Definition:Image (Set Theory)/Mapping/Subset

Definition
Let $S$ and $T$ be sets. Let $f: S \to T$ be a mapping.

Let $X \subseteq S$ be a subset of $S$.

Definition 2
Thus:
 * $\forall X \subseteq S: f \sqbrk X = \map {f^\to} X$

and so the image of $X$ under $f$ is also seen referred to as the direct image of $X$ under $f$.

Also see

 * Image of Singleton under Mapping
 * Image of Domain of Mapping is Image Set
 * Image of Subset under Mapping equals Union of Images of Elements


 * Definition:Direct Image Mapping of Mapping
 * Definition:Covariant Power Set Functor

Generalizations

 * Definition:Image of Mapping


 * Definition:Image of Relation
 * Definition:Image of Subset under Relation

Related Concepts

 * Definition:Preimage of Subset under Mapping
 * Definition:Preimage of Subset under Relation