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Topology of ...
Topology of pointwise convergence redirects to an eponym section of Pointwise convergence.
Topology of compact convergence redirects to Compact convergence.
But Topology of uniform convergence does not redirect to Uniform convergence. Instead, it redirects to Topologies on spaces of linear maps. Moreover, the topology of uniform convergence is not explicitly mentioned in Uniform convergence.
This sets several issues:
- Coherency of redirect targets
- As far as I know, the topology of uniform convergence is defined for a much larger class of functions than the linear maps.
- Topologies on spaces of linear maps is an article almost entirely written by Mgkrupa. This article is awfully written: almost no context provided; much too WP:TECHNICAL; for finding the definition of the topology of uniform convergence (the subject of the first section), one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before. So, for understanding the definition, one needs to be an expert of the subject, or to spend several hours of hard work.
What should be done with these issues? D.Lazard (talk) 17:18, 30 June 2022 (UTC)
- "one has to read a long list of formulas without prose before reaching a definition involving notations defined many lines before." I moved the section. Problem solved. Mgkrupa 17:45, 30 June 2022 (UTC)
- "the topology of uniform convergence is defined for a much larger class of functions than the linear maps." Yes, there should be an article about this topic. I suggest that someone (not me) change "Uniform convergence" from a redirect into an article about this topic. Or maybe change it into a disambiguation page. Mgkrupa 17:45, 30 June 2022 (UTC)
- Side note: I think that part of the reason by the article Topologies on spaces of linear maps is so technical is because there is no article dedicated to the more general theory of Uniform convergence for arbitrary classes of functions. If an article on this topic is created then we could link to it and simplify the presentation in Topologies on spaces of linear maps. Mgkrupa 18:12, 30 June 2022 (UTC)
- "much too WP:TECHNICAL" The article Topologies on spaces of linear maps was intended to be about the various topologies that are used in functional analysis, which necessarily involves concepts such equicontinuous sets, bounded subsets, the Mackey topology, the ε-topology, and so on. I would like the article to be less technical and would love to hear suggestions on how to accomplish this. Mgkrupa 18:00, 30 June 2022 (UTC)
- "almost entirely written by Mgkrupa. This article is awfully written" The article does need improvement. I suggest that we work together to improve it. Perhaps we can start by determining the best way to organize it? Mgkrupa 18:00, 30 June 2022 (UTC)
- The material is too specialized for the subject matter. So I think that the solution is to not give the most general formulation possible. For instance, the primary context could be the weak convergence of continuous linear maps between Banach spaces, as is the context for many of the most standard textbook references on functional analysis. (At present, it seems Banach spaces are not even mentioned on the page.) Having said that, I personally like the nature of much of your contributions to this page and other similar ones. But I might suggest it is more appropriate somewhere like nlab, where it is still easily accessible to those who want it, but where wiki can have a space for (what I would call) writing more encyclopedia than knowledge database. Gumshoe2 (talk) 19:16, 30 June 2022 (UTC)
- The Banach space cases should be mentioned. However, there are already multiple articles dedicated to such topologies. The article Operator topologies#List of topologies on B(H) lists many of them, including: Strong operator topology, Weak operator topology,Norm topology, Ultraweak topology, Ultrastrong topology, Weak convergence (Hilbert space), Weak topology. If I remember correctly, the reason why I originally created the article Topologies on spaces of linear maps was precisely because there was no article discussing uniform convergence in the general (non-normed space) setting of TVSs, and this was also why I did not add (norm space)-specialized content like what you suggested (i.e. weak convergence of continuous linear maps between Banach spaces). Having said that, this omission should be corrected as these cases are very important. I also suggest that links to articles like Operator topologies, Strong operator topology, etc. be mentioned early in the article (maybe the introduction) to help readers who are only interested in these special cases (and not the more general case) navigate to their desired article. [Update: I changed the introduction to contain a link to Operator topologies.] Mgkrupa 19:50, 30 June 2022 (UTC)
- One comment about Topologies on spaces of linear maps, but which also applies to other articles written by you. The references are not targeted enough. Example: footnote 6 refers to "Narici & Beckenstein 2011, pp. 371–423.", and is refered to from about 7 places. Pages 371-423 is a huge range of pages, a whole chapter maybe? Each place that refers to something in that chapter should refer to a specific result on a specific page of that chapter, instead of forcing the interested reader to read the whole chapter to figure things out. PatrickR2 (talk) 04:30, 1 July 2022 (UTC)
- You're right that large page ranges is bad practice. I have experienced the same problem you have (embarrassingly, a couple times with my own citations, which is why I've been doing that less frequently recently). But as you say, I should (and will) start making the page ranges more targeted. However, I sometimes include the proof or relevant definitions/author comments in a citation's page range. Is that considered bad practice?. Mgkrupa 21:42, 1 July 2022 (UTC)
- Not sure I understand what the last sentence is referring to. Can you give an example? PatrickR2 (talk) 23:30, 1 July 2022 (UTC)
- Consider "Grothendieck's Completeness Theorem" here: Complete topological vector space#Topology of a completion. The statement of the theorem was on page 176 (the proof is on the pages immediately after it). The citation for the theorem is given as "pp. 175−178" and this page range includes some - but not all - of the definitions/notation that are needed to understand the theorem as stated in that reference. The definitions of some the terms and notation that the reference used were defined elsewhere in hard to find locations (in this case as far away as pp. 151 and 157). If I didn't include these 2 pages then I think it likely that it would have been difficult for another person to verify that the statement and definitions were copied correctly. Now although in this particular case I used two separate citations (because of how many definitions were needed), there are occasionally other situations where this is not necessary and it would make much more sense to just use a single citation e.g. such as "pp. 151, 157, 175-176". I wish I could give a better example but I can't think of a better one off the top of my head. But did that clarify my question? Mgkrupa 08:15, 2 July 2022 (UTC)
- Mgkrupa That sound ok in this case. But in general, if we don't refer to other concepts defined elsewhere in the book, I think it would be perfectly fine to just cite the page where the theorem in given. It's up to the interested reader to figure out where the proof is and where the definitions of any used concepts are in that source. No need to do it for them. The interested reader will learn more by looking things up themselves. PatrickR2 (talk) 04:35, 5 July 2022 (UTC)
- Consider "Grothendieck's Completeness Theorem" here: Complete topological vector space#Topology of a completion. The statement of the theorem was on page 176 (the proof is on the pages immediately after it). The citation for the theorem is given as "pp. 175−178" and this page range includes some - but not all - of the definitions/notation that are needed to understand the theorem as stated in that reference. The definitions of some the terms and notation that the reference used were defined elsewhere in hard to find locations (in this case as far away as pp. 151 and 157). If I didn't include these 2 pages then I think it likely that it would have been difficult for another person to verify that the statement and definitions were copied correctly. Now although in this particular case I used two separate citations (because of how many definitions were needed), there are occasionally other situations where this is not necessary and it would make much more sense to just use a single citation e.g. such as "pp. 151, 157, 175-176". I wish I could give a better example but I can't think of a better one off the top of my head. But did that clarify my question? Mgkrupa 08:15, 2 July 2022 (UTC)
- Not sure I understand what the last sentence is referring to. Can you give an example? PatrickR2 (talk) 23:30, 1 July 2022 (UTC)
- You're right that large page ranges is bad practice. I have experienced the same problem you have (embarrassingly, a couple times with my own citations, which is why I've been doing that less frequently recently). But as you say, I should (and will) start making the page ranges more targeted. However, I sometimes include the proof or relevant definitions/author comments in a citation's page range. Is that considered bad practice?. Mgkrupa 21:42, 1 July 2022 (UTC)
- The material is too specialized for the subject matter. So I think that the solution is to not give the most general formulation possible. For instance, the primary context could be the weak convergence of continuous linear maps between Banach spaces, as is the context for many of the most standard textbook references on functional analysis. (At present, it seems Banach spaces are not even mentioned on the page.) Having said that, I personally like the nature of much of your contributions to this page and other similar ones. But I might suggest it is more appropriate somewhere like nlab, where it is still easily accessible to those who want it, but where wiki can have a space for (what I would call) writing more encyclopedia than knowledge database. Gumshoe2 (talk) 19:16, 30 June 2022 (UTC)
Endomorphism ring of an elliptic curve
The link in the title (as you can see) is red. I thought of redirecting it to elliptic curve, but as far as I can tell, that target has no info on the endomorphisms of elliptic curves (so the redirecting is unhelpful at best and misleading at worst). Is the topic not covered at all in Wikipedia (if so, that's very surprising.) -- Taku (talk) 08:32, 4 July 2022 (UTC)
Incidentally, the ring of differential operators also doesn't exist either (a special case is in differential operators but not the general one with the product given by the Leibniz rule with variable coefficients.) -- Taku (talk) 08:38, 4 July 2022 (UTC)
- @TakuyaMurata: The ideal target right now would be Complex multiplication or Complex multiplication#Abstract theory of endomorphisms. — MarkH21talk 13:42, 4 July 2022 (UTC)
- Thank you. As a short-term fix, this does seem to work although it probably makes sense that there is a standalone article or a section in the elliptic curve article on this topic. —- Taku (talk) 08:23, 5 July 2022 (UTC)
- Taku, When you create a redirect that you think should be expanded into an article, you can tag it with {{R with possibilities}}
- I do not know enough about the topic to create a short description for the redirect. Maybe someone from the project could take a look. · · · Peter Southwood (talk): 07:27, 6 July 2022 (UTC)
- Thank you. As a short-term fix, this does seem to work although it probably makes sense that there is a standalone article or a section in the elliptic curve article on this topic. —- Taku (talk) 08:23, 5 July 2022 (UTC)
RfC on Glossary of areas of mathematics
Glossary of areas of mathematics is an article that should concern all of use. Its state is presently awful. I have started an WP:RfC on inclusions criterias for this stand-alone list, at Talk:Glossary of areas of mathematics#RfC on inclusion criteria. Contributions are welcome. D.Lazard (talk) 15:28, 5 July 2022 (UTC)
- Some verifiable explanation or definition of what constitutes an "Area of mathematics" would be useful if such exists. This appears to be the main subject of contention. Cheers · · · Peter Southwood (talk): 07:10, 6 July 2022 (UTC)
Move of "Poincaré conjecture" to "Perelman's theorem"
A new user 廖培 (talk · contribs) has recently moved Poincaré conjecture to Perelman's theorem, since it is no longer a conjecture. I think this is unambiguously a bad move, since it is still (despite its status) universally called Poincaré conjecture and never called Perelman theorem; the user has simply decided that it ought to now be known as Perelman theorem instead. I don't understand well the technology of reverting page moves, hopefully someone else here does? Gumshoe2 (talk) 03:23, 10 July 2022 (UTC)
- Thanks for flagging this. I have reverted. Presumably bots will clean up the redirects. --Trovatore (talk) 03:52, 10 July 2022 (UTC)
- I suggest delete the Perelman theorem, because, as another example, I think the Geometrization conjecture are also known as Perelman theorem.--SilverMatsu (talk) 04:16, 10 July 2022 (UTC)
- Much thanks, Trovatore! SilverMatsu, I believe there is absolutely nothing called Perelman theorem with any consistency. From google search "Perelman theorem" could be a classification of Ricci solitons, sometimes it is the existence of Ricci flow with surgery, in principle it could be either the geometrization conjecture or the Poincaré conjecture, and (by same principle) could be many other major results from his papers besides. I think there should not be any redirect or disambiguation page for "Perelman theorem." Gumshoe2 (talk) 14:20, 10 July 2022 (UTC)
- Nominated for RfD. --SilverMatsu (talk) 16:37, 11 July 2022 (UTC)
- Much thanks, Trovatore! SilverMatsu, I believe there is absolutely nothing called Perelman theorem with any consistency. From google search "Perelman theorem" could be a classification of Ricci solitons, sometimes it is the existence of Ricci flow with surgery, in principle it could be either the geometrization conjecture or the Poincaré conjecture, and (by same principle) could be many other major results from his papers besides. I think there should not be any redirect or disambiguation page for "Perelman theorem." Gumshoe2 (talk) 14:20, 10 July 2022 (UTC)
- I’d make Perelman's theorem and Perelman theorem redirect to either Poincaré conjecture or to Grigori Perelman#Geometrization and Poincaré conjectures. –jacobolus (t) 17:42, 11 July 2022 (UTC)
- Is there evidence that these phrases are used in the wild for that? --Trovatore (talk) 19:32, 11 July 2022 (UTC)
- Searching Google scholar for "Perelman's theorem" finds it continued:
- ...that the metric projection of a non-negatively curved open manifold onto its soul is a well-defined Riemannian submersion (ProQuest 304537849, [1]); this seems to match Grigori Perelman#Comparison geometry.
- ...that shrinking breathers of Ricci flow on closed manifolds are gradient Ricci solitons (doi:10.1007/s12220-017-9974-1)
- ...that positively curved ancient solutions have vanishing asymptotic volume ratio and infinite asymptotic scalar curvature ratio ([2])
- So it definitely seems incorrect to redirect to Poincaré conjecture. If we had enough links for these other things we could consider making a dab page. —David Eppstein (talk) 20:25, 11 July 2022 (UTC)
- As a comparable example, both Wiles's theorem and Wiles theorem redirect to Fermat's Last Theorem (even though those terms are extremely rare in the literature even 25 years after the proof). The Poincaré conjecture is by far the most famous theorem proven by Perelman (since the mid 2000s and into the future, I would expect any use of the generic "Perelman theorem" to mean this, with other "Perelman theorems" named something more specific; for example in the three examples that David Eppstein found, the theorems there are explicitly called “Perelman’s Rigidity Theorem”, “Perelman's No Local Collapsing Theorem” and "Perelman’s Theorem on Shrinking Breathers in Ricci Flow" when introduced; none of these is presented as "Perelman's Theorem" without qualification). In a brief search of the current literature, there are a bunch of uses of "Poincaré–Perelman theorem" and a few direct uses of "Perelman theorem" to mean this result, but it is still commonly called the "Poincaré conjecture" after the proof, out of historical inertia. –jacobolus (t) 20:32, 11 July 2022 (UTC)
- OK, if/when that happens, we can make those redirects. Wikipedia is not supposed to drive adoption of terminology. (By the way, I don't think it's wrong to keep calling it the Poincaré conjecture, given that Poincaré did in fact conjecture it. The assertions that it "was" a conjecture and "is now" a theorem are, I think, just wrong; if it's a theorem now then it has always been a theorem, even before there were humans. The proof has always existed; the only thing that has changed is that we now know a proof. Being a conjecture is more temporal; it's not a conjecture until someone conjectures it. Still, I don't think it stops being a conjecture just because we now know that it's also a theorem. --Trovatore (talk) 20:49, 11 July 2022 (UTC)
- Adding redirects here seems easy and low-cost (low chance of causing confusion; does not make false implications; as just a redirect, does not give “undue weight” to some fringe/unestablished usage), while potentially helping some readers. If nothing else, it prevents people from trying to "helpfully" move the page there in the future. Titles to be redirected have a much looser standard than the text of articles: redirects are about helping people find what they are looking for, not telling them what terms are standard usage. If you think there will be some confusion about whether Perelman theorem should refer to Poincaré conjecture or Geometrization conjecture, then a redirect to Grigori Perelman#Geometrization and Poincaré conjectures should eliminate that concern. –jacobolus (t) 21:02, 11 July 2022 (UTC)
- "The Poincaré conjecture is by far the most famous theorem proven by Perelman". That does not preclude a disambiguation page. That can be the bolded primary meaning (cf the treatment at Rabbit (disambiguation)). SpinningSpark 17:44, 13 July 2022 (UTC)
- If we called Poincaré conjecture as Perelman's theorem, I think we miss the contributions of Stephen Smale and Michael Freedman.--SilverMatsu (talk) 04:36, 14 July 2022 (UTC)
- It really doesn't make any difference at all, for our current purposes, whether "Perelman's theorem" would be a good name. We shouldn't even be talking about that. I'm not at all a stickler for the rules on talk pages; I'm not objecting to you talking about what you find interesting. I just don't want it to get confused with what our articles should be called or what redirects/disambigs we should have and where they should point. --Trovatore (talk) 15:48, 14 July 2022 (UTC)
- OK, if/when that happens, we can make those redirects. Wikipedia is not supposed to drive adoption of terminology. (By the way, I don't think it's wrong to keep calling it the Poincaré conjecture, given that Poincaré did in fact conjecture it. The assertions that it "was" a conjecture and "is now" a theorem are, I think, just wrong; if it's a theorem now then it has always been a theorem, even before there were humans. The proof has always existed; the only thing that has changed is that we now know a proof. Being a conjecture is more temporal; it's not a conjecture until someone conjectures it. Still, I don't think it stops being a conjecture just because we now know that it's also a theorem. --Trovatore (talk) 20:49, 11 July 2022 (UTC)
- Searching Google scholar for "Perelman's theorem" finds it continued:
- Is there evidence that these phrases are used in the wild for that? --Trovatore (talk) 19:32, 11 July 2022 (UTC)
- While I agree that a move of Poincaré conjecture to Perelman's theorem is inappropriate, a disambiguation page with links to, e.g., Poincaré conjecture, Thurston geometrization conjecture, might be appropriate. --Shmuel (Seymour J.) Metz Username:Chatul (talk) 11:18, 12 July 2022 (UTC)
- I suggest delete the Perelman theorem, because, as another example, I think the Geometrization conjecture are also known as Perelman theorem.--SilverMatsu (talk) 04:16, 10 July 2022 (UTC)
Deletion review of Łukaszyk–Karmowski metric
This discussion may be of interest to the community here. XOR'easter (talk) 14:26, 14 July 2022 (UTC)