I have some basic but confusing problems:

Let A_{i be a closed subset of real vector space R}^{m}^{i}, B_{i}an open subset of real vector space_{R}^{m}^{i}, for 1<= i <= n.

1. Is the product A_{1}A_{2}...A_{n }closed?

2. Is the product B_{1}B_{2}...B_{n}open?