I don't think there is even a surjective continous function from to (I'm still trying to prove it though)
Can a homeomorphism exist between an open and a half open set?
(ie: (0,1) and [0,1))
I know that to be a homeomorphism, a bijection must exist, they must be continuous, and they must have a continuous inverse... Where to go from here?
The fact that 0 is not included within the first set, would that alone make it so that it is not homeomorphic?
Thus there exists no homeomorphism between A and B.