Material :Daly analysis 2.4.7. Let A be a subset of a metric space X. Given r E X, define the distancefrom r to A to bedist(r, A) = inf{d(r, y) : y E A}.2.4 Closed Sets61Prove the following statements.(a) If A is closed, then r E A if and only if dist(r, A) = 0.(b) dist(r, A) < d(r, y) + dist(y, A) for all r, y E X.(c) dist(r, A) – dist(y, A)| < d(x, y) for all r, y E X.Additionally, show by example that it is possible to have dist(r, A) = 0 evenwhen z ¢ A.II

Name: Material :Daly analysis 2.4.7. Let A be a subset of a metric space X.
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Description: Material :Daly analysis 2.4.7. Let A be a subset of a metric space X. Given r E X, define the distancefrom r to A to bedist(r, A) = inf{d(r, y) : y E A}.2.4 Closed Sets61Prove the following statements.(a) If A is closed, then r E A if and only if dis