If $ E \rightarrow X $ is a covering, then $ |\pi_1 (X)|$ divides to $ \chi (E) $

46 Views Asked by At

I want to prove that no finite group acts free in $ \mathbb{R}^n $ in the process I found the following doubt:

How can you prove that: If $ E \rightarrow X $ is a covering, then $ |\pi_1 (X)|$ divides to $ \chi (E) $?