Topology: An Inquiry-Based Approach

Given a topological space $X$ and a surjection $p$ from $X$ to a set $Y\text{,}$ we can use the topology on $X$ to define a topology on $Y\text{.}$ This topology on $Y$ identifies points in $X$ through the function $p\text{.}$ The resulting function on $Y$ is called a quotient topology. The quotient topology gives us a way of creating a topological space which models gluing and collapsing parts of a topological space.