How to prove CP^1 homeomorphic two-dimensional sphere [duplicate]

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.