Show that the map $\psi_{m,n}:S^1×S^1→S^1×S^1$given by $(z,w)→(z^m,w^n)$ where $mn≠0$ is a covering map.
My attempt is $\psi_n:S^1\to S^1$ given by $z\to z^n$ is a covering map for $n\neq0$.Similarly $\psi_m:S^1\to S^1$ given by $z\to z^m$ is a covering map.Now,use the theorem we get $\psi_n\times\psi_m:S^1×S^1→S^1×S^1$ that is $\psi_{m,n}$ is covering map.Is my attempt correct?