This is an exercise from Conway. I managed to prove the first part of (a), but I can't understand the second part of (a). How can it be possible that f(a) belongs to the boundary of Ω? By the Open Mapping theorem, I think both f(G-{a}) and f(G) are open sets... Or is there a possibility that the second part of (a) is a typo? Could anyone please help me?