Talk:Product topology
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the second definition, defining open sets as generated by counterimages of open sets in *each* Xi seems wrong, or maybe I have misunderstood.83.211.54.72 08:55, 18 October 2005 (UTC)
- Yes, I misunderstood, it's ok, sorry 83.211.54.72 08:57, 18 October 2005 (UTC)
A product of (non-empty) locally compact spaces will be locally compact exactly in the case all but finitely many are in fact compact
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Using the adele ring as an illustration of this - it is a so-called restricted product, union of such locally compact subspaces. Does restricted product have wider status?
Charles Matthews 10:14, 8 Nov 2003 (UTC)
[edit] Separation axioms
This article currently has a section of separation axioms; It states "every product of Ti spaces is Ti", etc. Clear, maybe for a finite product, or a countable product; are these true even when the index set is uncountable? If so, it would be nice to strengthen the wording of this section to indicate that the claims are true for any product, even uncountable products. linas 22:03, 20 November 2005 (UTC)
