Measure, Integration & Real Analysis · Problem 6E.4

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · interior-intersection

Problem

Prove or give a counterexample: If

V

is a metric space and

U, W

are subsets of

V

, then

(\operatorname{int} U) \cap (\operatorname{int} W) = \operatorname{int}(U \cap W)