Lebl-Basic-Analysis-I · Problem 7.2.13

Metric Spaces

Mathematics · open-and-closed-sets

Problem

Let

(X, d)

be a metric space. a) For every

x \in X

and

\delta > 0

, show

\overline{B(x, \delta)} \subset C(x, \delta)

. b) Is it always true that

\overline{B(x, \delta)} = C(x, \delta)

? Prove or find a counterexample.