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I'm a complete newbie to this section: book are quite complicated in terms. Also, there is a problem with formal building homeomorphism. So, I need to prove that $CP^1 \simeq S^2 $. How to do it formally?
By the way, as I understand, that $RP^1 \simeq S^1 $ as identification of diametrically opposite points. Maybe my problem use similar solution.