3.II.13B

If $X$ and $Y$ are topological spaces, describe the open sets in the product topology on $X \times Y$. If the topologies on $X$ and $Y$ are induced from metrics, prove that the same is true for the product.

What does it mean to say that a topological space is compact? If the topologies on $X$ and $Y$ are compact, prove that the same is true for the product.

*Typos? Please submit corrections to this page on GitHub.*