I'm reading a book of [1], and on pages 206 ~ 207 in Section 4.19, the authors gave 5 examples of a covering space for Riemann surfaces that we studies so far.
One of which is a covering space of a Riemann Surface of log(z), but didn't quite explain what a covering map is there.
Specifically, the text goes like
Riemann surface of log(z) is a covering surface of $\Sigma \setminus \{0, \infty \} $, with infinitely many sheets.
My question
I was not sure what a covering map here is..
My guess
As, log is going from the covering space to the base space, I assume the exponential map is a covering map here as it's going from the covering space to the base space as the inverse of log?
Am I guessing correctly..?
Reference
[1] Jones, Gareth A., and David Singerman. Complex functions: an algebraic and geometric viewpoint. Cambridge university press, 1987.