Basic Analysis I — Real Analysis · Problem 7.2.12

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · open-and-closed-sets

Problem

Finish the proof of Proposition 7.2.11. Suppose

(X, d)

is a metric space and

Y \subset X

. Show that with the subspace metric on

Y

, if a set

U \subset Y

is open (in

Y

), then there exists an open set

V \subset X

such that

U = V \cap Y