Measure, Integration & Real Analysis · Problem 6A.6

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · metric-spaces-closure-of-open-ball

Problem

(a) Prove that if

V

is a metric space,

f \in V

, and

r > 0

, then

\overline{B(f,r)} \subseteq \overline{B}(f,r)

. (b) Give an example of a metric space

V

f \in V

, and

r > 0

such that

\overline{B(f,r)} \neq \overline{B}(f,r)