Quotient topologies can often be visualized as gluing elements of a topological space together.
Let with the usual topology (as a subspace of the reals), , and be given by and for . Then under the quotient topology is homeomorphic to the circle. Indeed, we can visualize what happened as a gluing operation: the two endpoints of the interval were glued together to create a closed loop.
- C. Adams and R. Franzosa. Introduction to Topology: Pure and Applied. Upper Saddle River, NJ: Pearson Prentice Hall, 2008. p. 89