I just started learning about covering spaces and was hoping someone could fill in the details for me with this particular example.
We think of $S^1\subset\mathbb{C}$ and define $p_n:S^1\to S^1$ by $p_n(z)=z^n$. Then for all $n\in\mathbb{N}$, $p_n$ is a covering.
The hint is to observe that $S^1-${$x$} is evenly covered by $p_n$ for all $x\in S^1$, but I don't see why this is true, and I'm not sure why this would imply that $S^1-${$x$} is a covering. Could someone please explain?