Question: modern analysis. piecewise function with discrete metric 7. Let X * 0 be a set and consider the discrete metric d on X defined by

modern analysis. piecewise function with discrete metric

7. Let X * 0 be a set and consider the discrete metric d on X defined by d(p, q) = p q 0 p = q (a) Let p E X and r > 0. Describe the ball Br(p) of center p and radius r. (b) Show that any subset Y C X is open. (c) Show that X is compact if and only if X is finite

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