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(6) (15pt) Construct a diffeomorphism between the sphere minus the north pole and the south pole and the cylinder {(z,y, z) : 22 + y*

(6) (15pt) Construct a diffeomorphism between the sphere minus the north pole and the south pole and the cylinder {(z,y, z) : 22 + y* = 1}. Check what you construct is indeed a diffeomorphism

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