Question: (a) Let (X, d) be a metric space. Given a point x EX and a real number r > 0, show that A =

(a) Let (X, d) be a metric space. Given a point X E X and a real number r > 0, show that A = {y € X: d.x, y) > r} is open in

(a) Let (X, d) be a metric space. Given a point x EX and a real number r > 0, show that A = {ye X: d(x, y) > r} is open in X. (b) Suppose (X, d) is a metric space and f: X R is continuous. Show that A = {x X : |f(x)| 0. (c) Show that f (x) converges uniformly on [0, ). X x+n

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