Measure, Integration & Real Analysis · Problem 6E.8

L^p Spaces — Sheldon Axler

Mathematics — Measure Theory · intersection-dense-open-sets-dense

Problem

Suppose

(X, d)

is a complete metric space and

G_1, G_2, \ldots

is a sequence of dense open subsets of

X

. Prove that

\bigcap_{k=1}^{\infty} G_k

is a dense subset of

X