Talk:Product topology

message: 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)
replies: text: Yes, I misunderstood, it's ok, sorry 83.211.54.72 08:57, 18 October 2005 (UTC)

message: 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)
replies: text: We should get some short proofs for these, then we wouldn't be in doubt. --MarSch 12:53, 12 March 2007 (UTC)
thread_title:  Separation axioms 

message: Is the point space a unit of taking the topological product?
Like X \times \{0\} \cong X. 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)
thread_title:  unit for topological product 

message: The definition now reads
Let I be a (possibly infinite) index set and suppose Xi is a topological space for every i in I. Set X = Π Xi, the Cartesian product of the sets Xi. For every i in I, we have a canonical projection pi : X → Xi. The product topology on X is defined to be the coarsest topology (i.e. the topology with the fewest open sets) for which all the projections pi are continuous.  The product topology is sometimes called the Tychonoff topology.
So, am I to understand that for a topology to have a product topology, it has to be for a Cartesian product of topological spaces for index sets? Isn't it a little odd to have index sets that are not indexing something? PDBailey (talk) 03:32, 22 January 2009 (UTC)
replies: text: Looks fine to me. There is one index set, I which indexes the spaces Xi . Indeed Jmath666 (talk) 04:08, 22 January 2009 (UTC)
thread_title:  say what? 

message: The search "product space" directs here. Is the any way that there could be a disambiguation between this page and this other Product Space (http://en.wikipedia.org/wiki/The_Product_Space)?
Thanks!
18.111.59.229 (talk) 21:51, 10 May 2012 (UTC)
thread_title:  Product space page 

message: I think it should be the case to adopt a standard romanization of Ти́хонов. At the moment, all wiki articles seem to choose randomly Tikhonov Tychonoff Tychonov Tihonov Tichonov (..) Which is a bit embarrassing, even because wikipedia has very thorough articles about the rules of romanization. 
Note: all common methods transliterate И to 'i'; Х to either 'ch' or 'kh' or 'h'; ов to 'ov'.
The French romanization -off was initially very popular, but it seems it has been abandoned in current English use; besides, it seems incoherent transliterating in a language following a third language's rules. 
I would choose a version, e.g. following the AMS, and align to it. pma 09:34, 7 February 2021 (UTC)
thread_title:  Romanization of Ти́хонов