Definition 3

Let B be a nonempty topological space. A covering E of B is said to be Galois if it is connected and if, for every point $b$ of B, the operation of the group Aut$_B(E)$ of B-automorphisms of E on the fibre $E_b$ is transitive.

Let E be a Galois covering of a topological space B and let $p$ be its projection. The mapping $p$ is surjective (A, I, p. 56, def. 6); therefore the space B is connected. Consequently, the covering $(E, p)$ has a nonzero degree.