Theorem 15.1:

Suppose that $p: \tilde{X} \longrightarrow X$ is a covering projection. Then

(i)

The map $p$ is a local homeomorphism (see exercise 7, lecture 3).

(ii)

The function $p$ is an open mapping.

(iii)

The fibers $p^{-1}(x)$ are discrete for each $x \in X$.