Let $\displaystyle n\in\{0,1,2\} $ en $\displaystyle X_i$ is a $\displaystyle T_n$-space for each $\displaystyle i$.

I want to proof that the product of the $\displaystyle X_i$'s is also a $\displaystyle T_n$ space.

And if $\displaystyle X_i\neq\emptyset$ for all $\displaystyle i$ then the reverse implication is true.

Thanks