Basic Analysis I — Real Analysis · Problem 7.2.13

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · open-and-closed-sets

Problem

Let (X,d)(X, d) be a metric space. a) For every x∈Xx \in X and δ>0\delta > 0, show B(x,δ)‾⊂C(x,δ)\overline{B(x,\delta)} \subset C(x,\delta). b) Is it always true that B(x,δ)‾=C(x,δ)\overline{B(x,\delta)} = C(x,\delta)? Prove or find a counterexample.

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