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By way of an example, we consider in detail the complex projective line C ℙ¹. […] Thus via the function w_0 the complex projective line C ℙ¹ becomes identified with the extended complex plane (i.e. the ordinary complex plane with an additional point at infinity). 2..2.1 Theorem The complex projective line C ℙ¹ is diffeomorphic to the 2-dimensional sphere S².

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