The equivalence closure[1] of $\mathord {\sim }_{R}$ is the relation $\smash {\mathord {\sim }^{\mathrm{eq}}_{R}}$[2] satisfying the following universal property:[3]
- Given another equivalence relation $\mathord {\sim }_{S}$ on $A$ such that $R\subset S$, there exists an inclusion $\smash {\mathord {\sim }^{\mathrm{eq}}_{R}}\subset \mathord {\sim }_{S}$.
