I've been struggling with a question for a few days now and I was hoping for some help, the question is as follows:
f a homeomorphism of the Riemann sphere and D1 and D2 generalised disks with boundaries S1 and S2 respectively. Prove f(D1)=D2 then f(S1)=S2.
I am sure there is an argument to be made about the continuity of limits (limit of points in D1 to S1, and these points being taken to D2 whose limit is S2) but I am not sure how to phrase this, any help would be greatly appreciated :)