Basic Analysis I — Real Analysis · Problem 7.5.3

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Suppose

(X, d_X)

(Y, d_Y)

are metric spaces and

f : X \to Y

is continuous. Let

A \subset X

. a) Show that

f(\overline{A}) \subset \overline{f(A)}

. b) Show that the subset can be proper.