Lemma 2.5.1 (Open/Closed balls are Open/Closed sets ) Let (X, a be a metric space, ro E X, and r > 0.Then the boundary of both B,(xo) and B,(ro) is contained in {r €X: d(r, ro) = r}. %3D Hence, the open ball B,(xo) is open in X and the closed ball B,(xo) is closed in X

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