Measure, Integration & Real Analysis · Problem 6A.10

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · metric-spaces-closure-union

Problem

Prove or give a counterexample: If

V

is a metric space and

U, W

are subsets of

V

, then

\overline{U \cup W} = \overline{U} \cup \overline{W}