I have problems solving this seemingly straightforward question.
Let $q : X \rightarrow Z$ be a covering space. Let $p : X \rightarrow Y$ be a covering space. Suppose there is a map $r : Y \rightarrow Z$ such that $q = r \circ p$. Show that $r : Y \rightarrow Z$ is a covering space.
Could someone give me a hint? Of course I should pick some covering definition and show that $r$ indeed satisfies this.
Thank you