Definition:Quotient Topology

Definition
Let $T = \struct {S, \tau}$ be a topological space.

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

Let $q_\RR: S \to S / \RR$ be the quotient mapping induced by $\RR$.

Also see

 * Quotient Topology is Topology


 * Identification Topology


 * Identification Topology equals Quotient Topology on Induced Equivalence