Question

(5) Circle each abbreviation, O-open, plies to the given subset of S cC: C-closed, D domain, CP compact, which ap CD CP S,^ i....) (6) a) Use the formulas for chordal distance to show that χ[1/리, 1/22-11, 22], for any 21,22 E C. In other words, the reciprocal mapping R(z) l/s preserves the chordal distance between two points. (Here the definitions 1 /0 = oo. 1/00-0 apply.) b) Use the formula for inverse stereographic projection (Equation 1.7.1) to show that R(a) 1/zcorresponds to a certain rotation of the Riemann sphere. Why does this give another proof that x1/1,1/2x2]

Answer 1

"Circle each abbreviation) = open, C = closed, D = domain cp = compact which applies to the given subset S subset C S = C which is Domain S = {z: 1 <