Le U,V and W be algebraic varieries of finite dimensions (in the case I am really interested, U = IR, V and W are defined by a system of homogeneous polynomials in IR^{n+1}, but the question is more general).

Assume U x V and U x W are homeomorphic.

It is true that V and W are homeomorphic ?

Remark: V and W have the same Betti numbers as the Newton polynomials of the cartesian product is the product of the polynomials.