Definition:Euclidean Relation

Definition
Let $\mathcal R \subseteq S \times S$ be a relation in $S$.

Euclidean
$\mathcal R$ is Euclidean :
 * $(1): \quad \mathcal R$ is left-Euclidean

and:
 * $(2): \quad \mathcal R$ is right-Euclidean.