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

One wonders: Why the restriction to finite products? The power of the Tychonoff topology is precisely that it makes this theorem true for arbitrary products. &mdash; Lord_Farin (talk) 20:34, 20 July 2015 (UTC)


 * At the very end of the current version of the sufficiency proof, we need the maximum $M$ to be finite, which is only guaranteed if there is a *finite* number of spaces. However, I confess that I cooked up this proof myself and did not yet consult the literature. There may well be a better argument, which does not have this bootleneck. --S.anzengruber (talk) 08:26, 21 July 2015 (UTC)


 * The Tychonoff topology has all projections equal to the whole space except for finitely many factors, meaning the proof carries over without difficulty. &mdash; Lord_Farin (talk) 19:16, 21 July 2015 (UTC)