# Definition:Saturated Set (Equivalence Relation)/Definition 3

Let $\sim$ be an equivalence relation on a set $S$.
Let $T\subset S$ be a subset.
$T$ is saturated if and only if it is the preimage of some set under the quotient mapping:
$\exists V \subset S / \sim \; : T = q^{-1} \left[{V}\right]$