1. The problem statement, all variables and given/known data Let p: E-->B be a covering map. Let E be path connected and B be simply connected. Prove that p is a homeomorphism. 2. Relevant equations 3. The attempt at a solution I'm really struggling with this. Can anyone give me any insights? B is simply connected so any two paths with the same end points are homotopic and it's fundamental group is trivial. Help please?