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.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.8$: Quotient spaces: Definition $3.8.1$