Definition:Identification Topology/Identification Mapping

Definition
Let $\struct {S_1, \tau_1}$ be a topological space.

Let $S_2$ be a set.

Let $f: S_1 \to S_2$ be a mapping.

Let $\tau_2$ be the identification topology on $S_2$ with respect to $f$ and $\struct {S_1, \tau_1}$.

The mapping $f: S_1 \to S_2$ in this context is called the identification mapping.

Also known as
Some sources call $f$ the identification map while others call it the identification function. All roads lead to Rome.