\begin{definition}[Definition:Identification Topology/Identification Mapping]
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'''.
\end{definition}