Definition:Saturation (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.


The saturation of $T$ is the union of the equivalence classes of its elements:

$\displaystyle \overline T = \bigcup_{t \mathop \in T} \eqclass t \sim$