# Definition:Invariant Mapping Under Equivalence Relation

## Definition

Let $S$ and $T$ be sets.

Let $\mathcal R$ be an equivalence relation on $S$.

Let $f: S \to T$ be a mapping.

Then $f$ is invariant under $\mathcal R$ if and only if:

$x \mathrel {\mathcal R} y \implies f \left({x}\right) = f \left({y}\right)$