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.
Hatcher 1.3. problem 16
5
$\begingroup$
algebraic-topology
-
5Seems like it looks a lot like Lemma 80.2. in Munkres. – 2013-08-11