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.

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

Assume that $U \times V$ and $U \times W$ are homeomorphic. Is it true then 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.