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Question: exercise 2 from tao let x d be a metric...

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Exercise 2 (From Tao). Let (X, d) be a metric space, let Zo E X, r > 0 and let us consider the open ball B := {x e X : d(to,z) < r} and the closed ball C := {x E X : d(ro,x) r). Show that (1) B S C. Hint: use the previous exercise. (2) Give an example of (X,d), zo X and r 0 for which B C. Hint: you can use any property proven during the lectures
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