I have JUST been introduced to the Hilbert Space ($\displaystyle \ell^2$ space), and I have to show the following:

Prove that $\displaystyle ([-1,1]^{\infty},\Omega_p)$ is homeomorphic to the Hilbert Cube.

$\displaystyle \Omega_p$ is the product topology and the Hilbert Cube is a subspace of the Hilbert Space where each term of the sequences satisfies $\displaystyle |s_j| \leq \frac{1}{j}$.

I know that I need to build a homeomorphism between the two, but I'm not sure how to start this or what it would look like. Any help would be appreciated.