Category:Definitions/Identification Topology

This category contains definitions related to the identification topology.
Related results can be found in Category:Identification Topology.

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.

The identification topology on $S_2$ with respect to $f$ and $\struct {S_1, \tau_1}$ is defined as:

$\tau_2 = \set {V \in \powerset {S_2}: f^{-1} \sqbrk V \in \tau_1}$