Definition:Saturated Set (Equivalence Relation)/Definition 3

Definition

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:

$\exists V \subset S / \sim \; : T = q^{-1} \left[{V}\right]$