Most texts/videos on the subject don't go that carefully through the examples unless they're trivial. That doesn't help the beginner to understand the concept. But you started with the easiest examples, and gradually went to less trivial ones, following the exact procedure given by the definition and explaining everything in great detail. Thank you so much!
So helpful, thanks a lot;;; But I still have a question, can you explain me? The second example, S^2, I get all the steps we have to do, but when I tried to do the quotient I have some doubts.. In this case we have X1 and X2, and also D0 two times, D1 two times and D2 two times.. So we need to do the disjoint union of them all? I am not sure about this, cus it seems to be wrong when I think about the map... I dont know if I let my question undertandable, but if you could help me, it would be great. Anyway thanks, helped me to get the feeling about this
I get it, but if I would need to write the quotient, I would need to do the disjoint union of them all? I mean: X1 U X2 U D0 U D1 U D2 / x ~ \varphi(x) which U is disjoint union, and knowing that we have more than one D0, D1, D2...