Hatcher-Algebraic-Topology · Problem 1.3.1

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

For a covering space

p : \tilde{X} \to X

and a subspace

A \subset X

, let

\tilde{A} = p^{-1}(A)

. Show that the restriction

p : \tilde{A} \to A

is a covering space.