Are they topologically equivalent?

Question

Are ABCD topologically equivalent; are 4578 topologically equivalent?

Answer 1

No. Both ABCD and 4578 consist of four connected components. Can they be mapped onto one another? Any homeomorphism would map connected components to connected components. B and 8 are equivalent (two holes) But 5 and 7 are simply connected while only C is simply connected. And 4 has one hole while A and D have one hole.