Let $\{(X_\alpha,T_\alpha):\alpha\in{\lambda}\}$ be an indexed family of topological spaces, let $X=\prod_{\alpha\in{\lambda}}X_\alpha$, and let $T$ be the box topology on $X$. Then for each $\beta\in{\lambda}$, the projection map $\pi_{\beta}:X\to{X_\beta}$ is open.
- I would like to see a proof of this theorem please.