Definition:Saturation (Equivalence Relation)/Definition 1

Definition

Let $\sim$ be an equivalence relation on a set $S$.

Let $T\subset S$ be a subset.

The saturation of $T$ is the set of all elements that are equivalent to some element in $T$:

$\overline T = \{s \in S : \exists t\in T : s\sim t\}$