Question Define an infinitely long cylinder.
Definition: Quotient topology
Let $\left ( X,\tau \right )$ be a topological space. Let ~ be an equivalence relation on X and let $X^{*}$ be he collection of equivalence classes. Let $\pi: X\rightarrow X^{*}$ be the map taking each point to its equivalence class, i.e. $\pi\left ( x \right )=\left [ x \right ]$.
The quotient topology $\tau^{*}$ on $X^{*}$ is the collection of sets $U \subseteq X^{*}$ such that $\pi^{-1}\left ( U \right ) \in \tau$.
I am having a bit of problem beginning this question. A cylinder has a disc at the end. So perhaps there should be an $S^{1}=\left [ 0,1 \right ]$ we could work from?
However, any useful hints to kickstart me would be utmost helpful.
Thanks in advance.