Definition:Saturated Set (Equivalence Relation)/Definition 2

From ProofWiki
Jump to navigation Jump to search

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:

$\displaystyle \exists U \subset S : T = \bigcup_{u \mathop \in U} \left[\!\left[{u}\right]\!\right]$