Question: Let S = {(x, y, z) | x2 + y? + 2? =1} (a) Prove that SO = S {(0, 0, 1) } is

Let S = {(x, y, z) | x2 + y? + 2? =1} (a) Prove that SO = S \\ {(0, 0, 1) } is diffeomorphic to the cy-plane T in R. Hint: Stereographic projection: consider the maps ( : S" -> T given by o (@, y, z) = (7, 7 ,0) and : T -> S' given by v(X, Y, 0) = (- 2X 2Y 14X472 (b) Deduce that S" has an atlas which consists of just one allowable surface chart

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