# Category:Definitions/Preimages

This category contains definitions related to Preimage in the context of Set Theory.
Related results can be found in Category:Preimages.

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.

If no element of $Y$ has a preimage, then $f^{-1} \sqbrk Y = \O$.

## Subcategories

This category has only the following subcategory.

## Pages in category "Definitions/Preimages"

The following 21 pages are in this category, out of 21 total.