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

Prove that is homeomorphic to the Hilbert Cube.

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

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.