Hatcher-Algebraic-Topology · Problem 1.3.3

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Let

p : \tilde{X} \to X

be a covering space with

p^{-1}(x)

finite and nonempty for all

x \in X

. Show that

\tilde{X}

is compact Hausdorff iff

X

is compact Hausdorff.