Let $\displaystyle n \in \mathbb{Z^+}, X$ is nonempty.

(i) Find a bijective map $\displaystyle f: X^\omega \times X^\omega \rightarrow X^\omega$

(ii) If $\displaystyle A \subset B$ find an injective map $\displaystyle gA^\omega)^n \rightarrow B^\omega$

The cartesian product $\displaystyle A_1 \times A_2 \times ... $ is the set of all $\displaystyle \omega-$tuples of elements of $\displaystyle X$ is denoted by $\displaystyle X^\omega$.

I've tried many examples but none works... Can I get some help with these two please?