Category:Examples of Quotient Mappings

This category contains examples of Quotient Mapping.

Let $\RR \subseteq S \times S$ be an equivalence on a set $S$.

Let $\eqclass s \RR$ be the $\RR$-equivalence class of $s$.

Let $S / \RR$ be the quotient set of $S$ determined by $\RR$.

Then $q_\RR: S \to S / \RR$ is the quotient mapping induced by $\RR$, and is defined as:

$q_\RR: S \to S / \RR: \map {q_\RR} s = \eqclass s \RR$

for all $s \in S$.