I just started studying the quotient topology and equivalence relations as well, I have a question on this example which might make me understand more in general.
The interval $[0,1]$ with equivalent classes {$0,1$} and all singletons {$x$} $\in (0,1)$
When mapping $[0,1]$ with a quotient map onto the partition defined above, why is it a circle? I understand we are 'gluing' $0$ and $1$ into a single point, but more abstractly, how can I understand this?
Thank you