For each n E N, we write S" := {(r1, x2, . .. , Tn+1) E R"+1 : E 2 = 1}. Li=1 (1) Let f : S2 → R4 be the function f (x, y, z) = (x2 – y, xy, yz, xz). Define an equivalence relation - on S? by setting...

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Extracted text: For each n E N, we write S" := {(r1, x2, . .. , Tn+1) E R"+1 : E 2 = 1}. Li=1 (1) Let f : S2 → R4 be the function f (x, y, z) = (x2 – y, xy, yz, xz). Define an equivalence relation - on S? by setting (x1, Y1, 21) ~ (x2, Y2, 22) if and only if f(x1,Y1, 21) = f(x2, Y2, 22). Of the spaces you have encountered in the course thus far, determine which one is the quotient space S²/ ~? [Hint: To determine when (x1, Y1, 21) ~ (x2, Y2, 2) consider the case y1 = 21 = 0 first.]