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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.
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    Hint: use the standard basis for the box topology.2012-12-20

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