Definition:Saturated Set (Equivalence Relation)/Definition 2

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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 a union of equivalence classes:

$\ds \exists U \subset S : T = \bigcup_{u \mathop \in U} \eqclass u {}$