9. (a) Show that if x E Br(a), then there is an c > 0 such that
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9.
(a) Show that if x E Br(a), then there is an c > 0 such that the closed ball centered at x of radius c is a subset of Br(a).
(b) If a "# b are distinct points in X, prove that there is an r > 0 such that Br
(a) n Br
(b) = 0.
(c) Show that given two balls Br
(a) and Bs(b), and a point x E Br
(a) n Bs(b), there are radii c and d such that
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