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

Banach Spaces — Sheldon Axler

Mathematics — Measure Theory · metric-spaces-open-sets

Problem

Suppose

V

is a metric space. (a) Prove that the union of each collection of open subsets of

V

is an open subset of

V

. (b) Prove that the intersection of each finite collection of open subsets of

V

is an open subset of

V