Category:Definitions/Preimage of Subset under Mapping

This category contains definitions related to Preimage of Subset under Mapping.
Related results can be found in Category:Preimage of Subset under Mapping.

Let $Y \subseteq T$.

The preimage of $Y$ under $f$ is defined as:

$f^{-1} \sqbrk Y := \set {s \in S: \exists t \in Y: \map f s = t}$

That is, the preimage of $Y$ under $f$ is the image of $Y$ under $f^{-1}$, where $f^{-1}$ can be considered as a relation.