1. The problem statement, all variables and given/known data Find two spaces A,B compact where A and B are nonhomeomorphic but AX[0,1][tex]\cong[/tex]BX[0,1] 2. Relevant equations Definitions of homeomorphism, cardinality possiby, I have no idea where to start. 3. The attempt at a solution My idea Is [0,1] and S^1, but im not sure if the unit square is homeo to the cylinder.