Definition talk:P-Product Metric

There are other useful/important metrics on products of metrics. One, whose name I cant remember at the moment, defines $d(p,q) = \max \{d(p_i,q_i)\}$, and then there are others that work for countably infinite products. I kind of think this page should be renamed, new pages added, and perhaps a category created for metrics on product spaces. I'll try to work on that a bit tonight/tomorrow. --Dfeuer (talk) 02:13, 17 December 2012 (UTC)


 * The metric you mentioned is already mentioned; it is denoted $d_{\infty}$ on this page.


 * I don't see why this page should be renamed. Could you please explain?


 * Yes, maybe the subpage should be renamed in due course. There is already a  message at the bottom which basically reiterates some of what you are saying. I think you can feel free to make additions, but I don't really know what other contributors have in mind for this page now.


 * The category you appear to be thinking of seems to already exist as Category:Product Space; you might think that a rename is desirable. --abcxyz (talk) 02:56, 17 December 2012 (UTC)


 * The page should be renamed because it's not a definition; it's a list of related definitions. Category:Product space is too broad for my purpose: I was thinking of a subcategory for metrics on product spaces. I suspect it will be a small subcategory, but why not? Sorry I missed the d_\infty you mention. --Dfeuer (talk) 03:15, 17 December 2012 (UTC)


 * This type of merging several related definitions into a single page, with transclusions, is practiced all over this site. Examples include Definition:Set Union, Definition:Continuity, Definition:Homomorphism (Abstract Algebra), Definition:Increasing, and many others. Unless I'm missing something, there is basically equal merit in changing this page as in changing many of those. If you have an objection to this which is compelling enough (as it will be a large-scale change if it ever takes place), it probably belongs to the main talk page. As for me, I'm sorry, but I can't see anything wrong with the way it currently is.


 * The categories Category:Product Spaces and Category:Product Space do seem rather strange (and maybe potentially confusing). Perhaps we should replace these with Category:Product Spaces (Topology) and Category:Product Spaces (Metric Spaces)? I'd like some additional feedback before any action is taken. --abcxyz (talk) 03:35, 17 December 2012 (UTC)


 * They're only sort of related. They are all metrics inducing product topologies on topological products of spaces whose topologies are induced by metrics. There is, as far as I know, no notion of a product of metric spaces, per se. Unlike a number of other pages with related definitions, these definitions don't lead to isomorphic structures. I'm pretty new to PW, though, so I don't really know how things are usually done, but I have noticed that prime.mover likes to separate rather than combine whenever possible.--Dfeuer (talk) 03:47, 17 December 2012 (UTC)


 * Well then, I'm not sure. Comments on this from someone with access to the source works?
 * So what do you propose: have this particular page refer specifically to pairwise/finite products and a separate page for countably infinite products? --abcxyz (talk) 04:03, 17 December 2012 (UTC)


 * I was thinking more of having it refer specifically to $r$-products, and having other pages for various other metrics on products. Dfeuer (talk) 05:57, 17 December 2012 (UTC)