I'm trying to find the universal covering space of the Klein bottle. I know that $\mathbb R^2$ covers the Klein bottle , but I don't know how to prove, I found this proof on internet:
Someone knows why this quotient map is a covering map or have an alternative solution? I found this solution a little bit weird due my lack of experience on this subject, if fact, I'm a really beginner on that.
Please, I need help
Thanks