Symbols:Q/Quotient Mapping

Quotient Mapping

 * $q_\mathcal R$

The quotient mapping induced by $\mathcal R$:


 * $q_\mathcal R: S \to S / \mathcal R: \map {q_\mathcal R} s = \eqclass s {\mathcal R}$

where:
 * $\mathcal R \subseteq S \times S$ be an equivalence relation on a set $S$


 * $\eqclass s {\mathcal R}$ is the $\mathcal R$-equivalence class of $s$


 * $S / \mathcal R$ is the quotient set of $S$ determined by $\mathcal R$.

Also known as:
 * the canonical surjection from $S$ to $S / \mathcal R$
 * the canonical map or canonical projection from $S$ onto $S / \mathcal R$
 * the natural mapping from $S$ to $S / \mathcal R$
 * the natural surjection from $S$ to $S / \mathcal R$
 * the classifying map or classifying mapping (as it classifies the elements of $S$ into those various equivalence classes)
 * the projection from $S$ to $S / \mathcal R$