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)
- We should get some short proofs for these, then we wouldn't be in doubt. --MarSch 12:53, 12 March 2007 (UTC)
[edit] unit for topological product
Is the point space a unit of taking the topological product?
Like 
. This would mean that each space is homeomorphic to a product space. Thus each fiber bundle would be homeomorphic to a product, which would mean wording like "non-trivial product" would have to be used to characterize them.--MarSch 12:52, 12 March 2007 (UTC)
