(a) Let (X, d) be a metric space. Given a point x EX and a real...

 

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(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)| <r} is open in X for each r > 0. (c) Show that f (x) converges uniformly on [0, ∞). X x²+n² (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)| <r} is open in X for each r > 0. (c) Show that f (x) converges uniformly on [0, ∞). X x²+n²

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Solution let x d be a metric Space Giv... View the full answer