# Category:Euclidean Relations

This category contains results about Euclidean Relations.

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

$\mathcal R$ is left-Euclidean if and only if:

$\left({x, z}\right) \in \mathcal R \land \left({y, z}\right) \in \mathcal R \implies \left({x, y}\right) \in \mathcal R$

$\mathcal R$ is right-Euclidean if and only if:

$\left({x, y}\right) \in \mathcal R \land \left({x, z}\right) \in \mathcal R \implies \left({y, z}\right) \in \mathcal R$

$\mathcal R$ is Euclidean if and only if it is both left-Euclidean and right-Euclidean.

## Pages in category "Euclidean Relations"

This category contains only the following page.