Let x1, x2, … be a sequence of the points of the product space  Show that this sequence co...

Let x1, x2, … be a sequence of the points of the product space  Show that this sequence converges to the point x if and only if the sequence πα,(x1), πα,(x2), … converges to πα,(x) for each α. Is this fact true if one uses the box topology instead of the product topology?