Basic Analysis I — Real Analysis · Problem 7.3.1

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · sequences-and-convergence

Problem

Finish the proof of Proposition 7.3.13: Let

(X, d)

be a metric space and

A \subset X

. Let

p \in X

be such that there exists a sequence

\{x_n\}_{n=1}^\infty

A

that converges to

p

. Prove that

p \in \overline{A}