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

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

\Omega_p is the product topology and the Hilbert Cube is a subspace of the Hilbert Space where each term of the sequences satisfies |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.