Talk:Filter on Product Space Converges to Point iff Projections Converge to Projections of Point

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If I am nor wrong this :

By the definition of the natural basis, there is a finite set $J \subseteq I$ such that $\displaystyle U = \bigcap_{j \in J}U_j$ where $U_j \subseteq X_j$ is an open set for all $j \in J$.

to this

By the definition of the natural basis, there is a finite set $J \subseteq I$ such that $\displaystyle U = \bigcap_{j \in J} \pi^{-1}(U_j)$ where $U_j \subseteq X_j$ is an open set for all $j \in J$.

Sorry if I am mistaken.

Looks plausible. Thank you for the correction. --prime mover 07:16, 21 August 2011 (CDT)