Answer: Let (R2, d) be the metric space whose distance d(P1, P2) between two points P1 =
Chapter 16, Problem 16.12(choose chapter or problem)
Let (R2, d) be the metric space whose distance d(P1, P2) between two points P1 = (x1, y1)and P2 = (x2, y2) in R2 is defined by d(P1, P2) = (x1 x2)2 + (y1 y2)2 and let d bethe discrete metric, that is,d(P1, P2) = 0 if P1 = P21 if P1 = P2.Verify each of the following.(a) The function f : (R2, d) (R2, d) defined by f(x, y)=(x, y) is continuous.(b) The function g : (R2, d) (R2, d) defined by g(x, y)=(x, y) is not continuous.
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