Basic Analysis I — Real Analysis · Problem 7.4.18

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · completeness-and-compactness

Problem

Let

(X, d)

be a metric space and

K \subset X

. Prove that

K

is compact as a subset of

(X, d)

if and only if

K

is compact as a subset of itself with the subspace metric.