Basic Analysis I — Real Analysis · Problem 7.5.13

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · cluster-points-metric-spaces

Problem

Let

(X,d)

be a metric space,

S \subset X

, and

p \in X

. Prove that

p

is a cluster point of

S

if and only if

p \in \overline{S \setminus \{p\}}