Hatcher-Algebraic-Topology · Problem 1.3.16

The Fundamental Group

Mathematics — Graph Theory · covering-spaces

Problem

Given maps

X \to Y \to Z

such that both

Y \to Z

and the composition

X \to Z

are covering spaces, show that

X \to Y

is a covering space if

Z

is locally path-connected, and show that this covering space is normal if

X \to Z

is a normal covering space.