Definition:Trivial Quotient

Definition

Let $\Delta_S$ be the diagonal relation on a set $S$.

As $\Delta_S$ is an equivalence, we can form the quotient mapping:

$q_{\Delta_S}: S \to S / \Delta_S$.

This quotient mapping is called the trivial quotient of $S$.

Also see

• Trivial Quotient is a Bijection

Sources

• 1967: George McCarty: Topology: An Introduction with Application to Topological Groups ... (previous) ... (next): Chapter $\text{I}$: Sets and Functions: Quotient Functions