Basic Analysis I — Real Analysis · Problem 7.5.8

Metric Spaces — Jiri Lebl

Mathematics — Real Analysis · continuous-functions

Problem

Let

(X, d_X)

and

(Y, d_Y)

be metric spaces and

f : X \to Y

be a one-to-one and onto continuous function. Suppose

X

is compact. Prove that the inverse

f^{-1} : Y \to X

is continuous.