Wikipedia:Articles for deletion/Stereotype space

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was redirect Stereotype space to Reflexive space#Other types of reflexivity, Stereotype algebra to Topological algebra, and Stereotype group algebra to Group algebra of a locally compact group. I leave it to the editors of these individual articles to make any adjustments needed to suit these incoming redirects. BD2412 T 17:44, 23 April 2020 (UTC)[reply]

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Stereotype space (edit | talk | history | protect | delete | links | watch | logs | views) – (View log · Stats)

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Stereotype algebra (edit | talk | history | protect | delete | links | watch | logs | views)

Stereotype group algebra (edit | talk | history | protect | delete | links | watch | logs | views)

I cannot find enough literature to establish the notability of this notion. Googling with ""stereotype space" -Akbarov" yields essentially no work on this notion. There is [1] which has an entry on "stereotype space" but the source of this book seems to be the Wikipedia article topological vector space. *Mathematically*, the notion looks interesting and so it should be ok to have some discussion of this notion elsewhere in Wikipedia if the sources can be acquired, perhaps without the term "stereotype space". Another option is to move the article to nlab where the notability requirement is less stringent. -- Taku (talk) 11:47, 8 April 2020 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. Coolabahapple (talk) 22:25, 9 April 2020 (UTC)[reply]

• Keep-the concept is cited in this paper:[2]. I think the concern was that the author of the papers was a crackpot or crank. If this concern was true, you wouldn't see a paper of his being cited by others in reputable literature.--Epiphyllumlover (talk) 23:00, 9 April 2020 (UTC)[reply]

  That one of the main references has been cited once by a different paper, which itself has only ever been cited once (by its own author), is not a very strong reason to keep a WP article. — MarkH₂₁^talk 20:12, 15 April 2020 (UTC)[reply]

  I agree with MarkH21 here. XOR'easter (talk) 20:15, 15 April 2020 (UTC)[reply]

• Delete per nom, and also because "mathematicians did not form a general opinion as to which term is more convenient, some do not use any term at all, and in addition, this class has been opened and reopened many times". This quote by the main opponent to deletion shows clearly that the term "stereotype space" is not notable by itself. The notability of the associated concept (topological space that is isomorphic to its bidual) is less clear. The defining property is evidently interesting for everybody who works on topological spaces. So, Topological vector space could have section on this subject, and all names that have been given to this property could be redirected there. For deserving having its own article, such a concept should either having been studied by many people (this is not the case here), or it should have been useful outside the strict study of the concept. No evidence has been given that this is the case here. Therefore I support deletion. D.Lazard (talk) 18:01, 14 April 2020 (UTC)[reply]

@D.Lazard: two questions:

For deserving having its own article, such a concept should either having been studied by many people (this is not the case here)

How many people had to study this class of spaces so that in your opinion it became notable?

or it should have been useful outside the strict study of the concept. No evidence has been given that this is the case here.

There is a section in the article devoted to applications. Why don't you count it? Eozhik (talk) 19:38, 14 April 2020 (UTC)[reply]

D.Lazard, Could you work at adding a section to Topological vector space, even now? In particular, the stereotype space article has more equations than the topological vector space article, and appears to be more developed. Can you bring topological vector space to a similar, or even better level?--Epiphyllumlover (talk) 19:44, 14 April 2020 (UTC)[reply]

For me, being "useful outside the strict study of the concept" means the use by others than the inventor of the concept, or the solution of a problem that has been set before the invention of the concept. In the section on applications, I see only generalizations and reference to works by the inventor of the concept and his frends, not the solution of pre-existing problems. D.Lazard (talk) 20:17, 14 April 2020 (UTC)[reply]

@D.Lazard: constructing duality theories for non-commutative groups is a pre-existing problem. And this problem is far from a final solution. That is why the "inventor and his friends" find support from colleagues abroad (and publish their results in reliable journals). Eozhik (talk) 20:41, 14 April 2020 (UTC)[reply]

• Comment Wikipedia policy WP:PRIMARY say Do not base an entire article on primary sources, and be cautious about basing large passages on them. As this article is based only on primary sources, this is sufficient for deleting it, without examining its notability. D.Lazard (talk) 20:17, 14 April 2020 (UTC)[reply]

There are secondary sources in the article as well. Eozhik (talk) 20:41, 14 April 2020 (UTC)[reply]

• Delete Redirect to Reflexive space#Other types of reflexivity: Per the arguments made by Taku and D.Lazard, this is not a term widely-used by independent secondary sources to the point that WP:GNG is not met and WP:NEOLOGISM can apply.
  Once could argue for a merge to topological vector space, the greater class of objects for which there is substantial secondary sources and standard terminology, but very little content in this article should be merged there on the basis of WP:DUE. — MarkH₂₁^talk 01:48, 15 April 2020 (UTC); changed to redirect 03:49, 22 April 2020 (UTC)[reply]

  MarkH21 this sounds as if there was a controversy between people who prefer to use the term "stereotype" and those who use other terms. There is no such a controversy: people use differenct terms, and this is normal for mathematics. For example, some people use the term linear mapping while others linear operator, and there are no misunderstandings between them. Similarly people use different notations. Eozhik (talk) 06:44, 15 April 2020 (UTC)[reply]

  I didn't say anything about there being a controversy. There just needs to be evidence that the term is widely used. In the evidence that you provided (currently in image form), I see four total articles that mention the term. But one of them has you as a co-author and one of them only says that Akbarov calls them stereotype spaces. That's not really evidence that many people use the term. For linear mapping and linear operator, we can easily find thousands of different independent sources that use each term. — MarkH₂₁^talk 19:27, 15 April 2020 (UTC)[reply]

  MarkH21, it’s not my fault that Wikipedia has no rule regulating how many references there should be. And it’s not my fault that when I posted this article 7 years ago nobody warned me. This is what I am talking about here. If these details were indicated in the rules, this would save everyone present from unnecessary waste of time. Eozhik (talk) 12:43, 16 April 2020 (UTC)[reply]

  However, MarkH21, there is still a possibility to edit this article by adding there the term "polar reflexive space" from G.Köthe's book. The relations between these two terms are the same as between linear map and linear operator. This would resolve this local problem, although, of course, the global one (concerning the rules) will remain actual. Eozhik (talk) 13:06, 16 April 2020 (UTC)[reply]

  The notability guidelines are intentionally vague so that we may rely on editor consensus instead of rigid numerical rules. If we had "more than 10 independent secondary sources use the term", for instance, what if there were 9 Annals papers from 9 different renowned mathematicians dedicated to the term and its theory and a Fields Medal awarded to someone for developing its theory? That's very different from 11 papers from two mathematicians publishing in an obscure journal that only briefly mention the term. Having rigid rules would prevent us from properly assessing the merits of a topic and would make WP overly inflexible. — MarkH₂₁^talk 13:18, 16 April 2020 (UTC)[reply]

  MarkH21 is exactly correct here. As I wrote below, trying to invent numerical scales and thresholds is likely to create an illusion of precision rather than actual clarity. XOR'easter (talk) 13:31, 16 April 2020 (UTC)[reply]

  And by flexibility you mean the possibility to kill other people's work without any legitimate reason. And to advertise the work of the people that you liked, also without being bothering with formalities. I have an opposite opinion. There must be clear rules that allow people to play fair game independently of whether they are your friends or not, whether they live in Europe, America, Russia etc., whether they have enough money to publish their own journals or not. Those who have these money, have the possibility to advertise themselves without Wikipedia. Eozhik (talk) 13:43, 16 April 2020 (UTC)[reply]

  Please, let's assume a measure of good faith here. Nobody is out to "kill" anything. We're not trying to stop anyone from posting on the arXiv, or publishing in journals, or writing a textbook, or expanding the nLab's entry on stereotype spaces. We're not even objecting to having material about stereotype spaces in another article, like topological vector space. We're just trying to decide, honestly and as fairly as we can, whether having three whole dedicated articles — stereotype space, stereotype algebra, stereotype group algebra — is the right course of action. As MarkH21 explained, if the Wikipedia community relied upon numerical rules like "a topic must be mentioned in 10 different journal articles" or "a paper must be cited at least 15 times", then people could just game those rules, just like they already game their impact factor and h-index. Making the rules sound exact does not mean that people will play fair. We rely upon community discussion because we believe that building an encyclopedia is too important for metrics that are only superficially precise. XOR'easter (talk) 15:06, 16 April 2020 (UTC)[reply]

  XOR'easter I spent a lot of time for creating and editing these articles. When doing this I was sure that this is legitimate and nobody will destroy my work. Because this is in human culture that if something does not contradict the laws, it is legitimate. And these articles are important for us since they give us a possibility to explain to our colleagues what we are doing (there are not so many possibilities, you can trust me). Even nLab, although being a very good website, is not so good since there are technical problems with pictures there (as far as I know). You compare this with h-index and impact factor, but the difference is that to play those games people already should have a good support from their countries: the possibilities to publish their own journals, to visit conferences, etc. for being successful. A mathematician living in Russia, or in Georgia, or in Uzbekistan is not in the same conditions as the one who lives in USA (and who because of this can easily enter the necessary clubs). Of course, nobody of us will refuse to use arXiv or to publish our works in normal journals after this story. But what happens here is not fair. And this contadicts human understanding of decency. Even h-index and impact factor are more fair, since they are based on clear rules. Eozhik (talk) 15:56, 16 April 2020 (UTC)[reply]

  I am not against merging this with other articles like topological vector space and topological algebra (although I foresee problems since these articles are only drafts). Another possibility, as I told already, is to add the term "polar reflexive" to the article with the references to Köthe and other authors. But what I definitely don't like is the idea to kill everything. On the base of suspicions. Eozhik (talk) 16:38, 16 April 2020 (UTC)[reply]

  It's naturally disappointing if something that you have worked on is nominated for deletion, but the general notability guideline has always been clear (including in 2012) that the most basic metric is significant coverage in reliable sources that are independent of the subject. There's not really much of that in this case, with perhaps one(?) example in the Kuznetsova article. If there is a lot of coverage from Russian, Georgian, or Uzbek mathematicians (or journals), the outcome is the same as if the coverage is from American mathematicians; there's no difference here. The article deletion discussions on WP are quite fair and based on logical arguments. — MarkH₂₁^talk 16:36, 16 April 2020 (UTC)[reply]

  MarkH21 formally these requiremets are met. "More than a trivial mention", "reliable", "secondary sources", "independent of the subject", the only vague point is "presumed". The rules must be more clear. And your idea of "flexibility" is not convincing. Eozhik (talk) 16:55, 16 April 2020 (UTC)[reply]

  I see only one reference (Kuznetsova) that can be considered significant coverage and independent, not multiple. Also, this "flexibility" isn't my idea; the guidelines were agreed upon via the consensus of many many WP editors over many years. — MarkH₂₁^talk 17:15, 16 April 2020 (UTC)[reply]

  MarkH21 what are you looking for? These spaces are studied by different authors. Some of them, like Smith, don't use any terms at all, some, like Brauner, use the term "p-reflexive", some, like Garibay Bonales, Trigos-Arrieta, Vera Mendoza, Hernandez, write "polar reflexive", some, like me, Kuznetsova, Aristov, Shavgulidze, use the term "stereotype". Some study algebras (stereotype or topological). There are mutual references. Are you speaking about generalizations of my own results? They are in the works by Aristov, Kuznetsova and Shavgulidze. Eozhik (talk) 17:54, 16 April 2020 (UTC)[reply]

  For multiple published papers not written by you or your co-authors that explicitly use the term stereotype ____ in-depth (i.e. not just Akbarov calls them "stereotype ____"). — MarkH₂₁^talk 21:57, 16 April 2020 (UTC)[reply]

  Stylistically it would be good to add here: "...and not by people who are familiar with you". MarkH21 this is the situation when mathematicians in different countries use different terms. This often happens, I told this already when I gave the example of linear mapping and linear operator. As far as I understand, adding to the article another, equivalent term, "polar reflexive space", will not satisfy you, right? Eozhik (talk) 22:10, 16 April 2020 (UTC)[reply]

  Perhaps merging this to Topological vector space or Reflexive space is more appropriate, although I see that the latter already has a section on this. I'm not sure whether "stereotype space" and "polar reflexive space" are collectively notable enough for an article, although even in that case one must determine a title based on WP:COMMONNAME, but that's a separate issue. — MarkH₂₁^talk 07:57, 18 April 2020 (UTC)[reply]

I don't understand what happens and what to do with these pictures. Eozhik (talk) 06:44, 15 April 2020 (UTC)[reply]

I agree with Sandstein that, except for really involved people, nobody want to read these walls of texts. Therefore, I have collapsed the long technical discussion that follows the nomination and does not contain clear policy-based arguments. Remains uncollapsed the nomination, the comments and !votes that are opened by a bolface header, and their answers.

In summary, so far, three editors support deletion, TakuyaMurata (the nominator), MarkH21 and D.Lazard (myself). Two editors are for keeping the article, Epiphyllumlover and Eozhik, the latter having a blatant WP:COI, being the author of the WP article and the author of its main references. D.Lazard (talk) 09:08, 15 April 2020 (UTC)[reply]

D.Lazard, Sandstein explained his motives to me differently, not like you:

except for really involved people, nobody want to read these walls of texts

For me the rules of this game remain unclear, what I find very strange. In particular, you did not comment this:

How many people had to study this class of spaces so that in your opinion it became notable?

Eozhik (talk) 09:41, 15 April 2020 (UTC)[reply]

Sandstein's comment is about the upload of copyrighted images. "Walls of text" is about the whole discussion that I have collapsed. By the way, this page is not for personal discussions between editors. So, I do not answer here to any personal question. D.Lazard (talk) 10:38, 15 April 2020 (UTC)[reply]

D.Lazard, this is not a personal question, this concerns the rules of Wikipedia. If you write that your vote is based on this opinion

For deserving having its own article, such a concept should either having been studied by many people (this is not the case here)

— while there is no rule that establishes the standards, it is natural that interlocutor asks you where you find these standards. Eozhik (talk) 13:30, 15 April 2020 (UTC)[reply]

• Delete The topic seems to lack notability in independent sources such as the Encyclopedia of Mathematics. Andrew🐉(talk) 10:04, 15 April 2020 (UTC)[reply]

Andrew, Eozhik noted that the term "stereotype" is used by Russians more. I am hoping he will share some of these foreign journals with us and translate it for us. It is possible that differences in terminology between the Encyclopedia of Mathematics and Eozhik could be due to language.--Epiphyllumlover (talk) 16:52, 15 April 2020 (UTC)[reply]

@Epiphyllumlover: Could be. But it is true that we cannot find a general reference work that gives the definition of a stereotype space. Of course, Google can miss some references, especially off-lines but so far we are not presented evidence that the notion has gained a general currency in the mathematics community. —- Taku (talk) 19:26, 15 April 2020 (UTC)[reply]

This is not true. Epiphyllumlover actually, all Russian mathematical journals (at least important ones) are translated into English, so there is no necessity to translate anything (thank god). Moreover, almost all recent papers are translated now by the authors and posted in arxiv.org. Most of the articles I refered to as well. That is why I have doubts that still (after removal those pictures) there is a necessity to give the quotations. As XOR'easter said,

I expect the people who participate in a deletion debate for a fairly abstruse mathematical topic to be conscientous and check into the available sources, even if it requires clicking a mouse button to expand a section of text.

(He meant clicking this Wikipedia page, but the difference is not too great, I believe.) The absense of this term in Encyclopedia of Mathematics is explained by the fact that after collapse of the Soviet Union (I am not its fan, but the problem exists) mathematics and mathematicians are not well-payed, and there is not enough money for publishing many mathematical books, including encyclopedias. Eozhik (talk) 12:23, 16 April 2020 (UTC)[reply]

Coolabahapple what does this mean:

• Comment--the best evidence of notability (that is, the list of citations and the images) is now collapsed. This risks rendering the whole deletion discussion illegitimate and I expect that it could be overturned should Eozhik wish to pursue deletion review.--Epiphyllumlover (talk) 16:52, 15 April 2020 (UTC)[reply]

  Eozhik should just post quotes and links, not copyvio images. The removal of copyvio images isn’t a reason for DRV. — MarkH₂₁^talk 17:09, 15 April 2020 (UTC)[reply]

  The images are significantly worse for discussion purposes than simple quotations of text, not least because it's harder to tell how many of them come from the same source. XOR'easter (talk) 18:21, 15 April 2020 (UTC)[reply]

  Everybody can read the collapsed part of the discussion by clicking on the button "show" on the right. D.Lazard (talk) 17:28, 15 April 2020 (UTC)[reply]

  Pretty sure you wouldn't like it if someone collapsed your best arguments. (But they tend not to read it and that is the point of collapsing.) And (directed to XOR'easter), the citations were collapsed too. Is the purpose of inexperience with the methods of this website to give a tactical advantage to an opposer? Or is it to learn? Do you expect the closer to enable this sort of thing?--Epiphyllumlover (talk) 19:48, 15 April 2020 (UTC)[reply]

  I expect the people who participate in a deletion debate for a fairly abstruse mathematical topic to be conscientous and check into the available sources, even if it requires clicking a mouse button to expand a section of text. And I expect those people to organize their thoughts sufficiently well that they can articulate a reason to keep or delete the article that is grounded in Wikipedia's policies and guidelines, providing an honest evaluation in terms that someone who does not specialize in the mathematics can still understand. I expect that mathematicians and scientists can do what I do and recognize that not every idea I have thought up and published necessarily belongs in an encyclopedia yet. I expect that scholars can appreciate how evaluating research work can be difficult, and that trying to invent numerical scales and thresholds is likely to create an illusion of precision rather than actual clarity. I expect that intellectuals can summon the emotional maturity not to treat a discussion about how to organize an encyclopedia like it is a battlefield. XOR'easter (talk) 20:04, 15 April 2020 (UTC)[reply]

  Sorry, the only statement I intended to direct you specifically was that the citations were collapsed too.--Epiphyllumlover (talk) 20:32, 15 April 2020 (UTC)[reply]

  Correct me if I am wrong, but no non-primary sources that are not already listed at stereotype spaces are presented at this discussion so far. So no key sources are hidden. —- Taku (talk) 21:24, 15 April 2020 (UTC)[reply]

  To find them go to "Technical discussion continued" and uncollapse it. The relevant part of the discussion can be found by doing a browser search for " Kuznetsova "--also see the screenshots slightly below the Kuznetsova and other citations.--Epiphyllumlover (talk) 00:45, 16 April 2020 (UTC)[reply]

  @Epiphyllumlover: I think the key phrase was not already listed at stereotype spaces. The Kuznetsova and Hernández–Trigos-Arrieta sources are both referenced in the article already. The assumption is that anyone looking at this AfD would look at the reference list. — MarkH₂₁^talk 01:47, 16 April 2020 (UTC)[reply]

(Further) comment. Fondamentally, this article is about duality in topological vector spaces. There are a Groethendieck's master work and a Bourbaki's book on topological vector spaces. I have not read them, but I do not imagine that they do not study duality, since duality was fundamental for both authors. None is mentioned in this article, even in the history section. I suspect that many of the theorems that appear in the article can be found in these works, although they are all presented as found by Akbarov. Whether I am wrong or not is not important, as, in any case, the article is biased as not giving any indication of what is really new in Akbarov theory, and what has been discovered by previous authors. This makes the article purely self-promotional. D.Lazard (talk) 13:36, 16 April 2020 (UTC)[reply]

This is the most impressive sentence:

Whether I am wrong or not is not important

It's not enough to suspect, D.Lazard:

I suspect that many of the theorems that appear in the article can be found in these works, although they are all presented as found by Akbarov.

In such cases, it is considered necessary to provide evidence. And you can send protest to the journals where this is published. Eozhik (talk) 13:58, 16 April 2020 (UTC)[reply]

Was the term in use during the soviet era? Do you have any of these soviet era offline works laying around? If so, please cite them for us and give short quotes.--Epiphyllumlover (talk) 19:43, 16 April 2020 (UTC)[reply]

Epiphyllumlover, no, as far as I know, in Soviet Union people did not study this class of spaces. And the term "stereotype space" appeared in 90ies. But I don't understand this concern about the term. It is usual in mathematics that people suggest new terms. For example, the term quantum group appeared not long ago. I only heard it in 90ies. Outside of Russia these spaces were called "polar reflexive spaces". The book by Köthe was not translated into Russian, that is why it did not occur to anybody here to use this combination of words. And that is why it did not occur to me to mention this in the article. Eozhik (talk) 20:19, 16 April 2020 (UTC)[reply]

If you have offline 90's era Russian sources using the term, could you cite them for us and give short quotes? Epiphyllumlover (talk) 20:23, 16 April 2020 (UTC)[reply]

I have edited the format of Eozhik's post for making understandable the change of paragraphs. I hope to not having changed the meaning.

Please, do not discuss other's posts, discuss the content of the article. For being clear, my point is firstly that there are important results on duality of topological vectors published by Grothendieck, Bourbaki, and other members of Bourbaki group ("important" is not my own opinion, as these result are a part of the motivation of Grothendieck's Field medal). Secondly, these results are not cited in the articles. Thirdly nothing is said in the article for distinguishing Akbarov own results from those that must be credited to others (the fact that Akbarov papers have been accepted by editors means that some results are new, not that they are all new). Thus the Wikipedia article does not follows the Wikipedia policy of neutral point of view (see WP:NPOV). None of these points is addressed in Eozhik's answer. D.Lazard (talk) 20:43, 16 April 2020 (UTC)[reply]

D.Lazard, it would be good if you would not edit my text. It is not yours. There is no intersection between the results listed in the article and Bourbaki's texts. This happens in mathematics. Eozhik (talk) 21:02, 16 April 2020 (UTC)[reply]

Agreed that D.Lazard should not edit Eozhik's posts. I hope Eozhik will not be too distracted by this to answer my question about whether he has offline 90's era Russian sources using the term and if he could you cite them for us. To D.Lazard: If we do not delete the article, maybe it can be improved somewhere along the lines you suggest. I think there could be room for compromise.--Epiphyllumlover (talk) 21:22, 16 April 2020 (UTC)[reply]

Epiphyllumlover, no, I don't know papers in Russian where this term is used (and which don't belong to our group). But you know, it seems to me you take what happens more serious than I do. This is not the end of the world. I just wanted to do what I can, and that is all. Eozhik (talk) 21:33, 16 April 2020 (UTC)[reply]

(edit conflict) D.Lazard has a valid point that several of the results come from elsewhere, e.g. basically all of the Examples section. The claim that There is no intersection between the results listed in the article and Bourbaki's texts is dubious: Chapter IV of Bourbaki's Topological Vector Spaces has significant intersection, including several entire sections after section 3 which begins with: A locally convex space E is said to be reflexive if the canonical mapping c_E from E into E" is a topological vector space isomorphism from E onto the strong dual of E_b^~. Some of the example in this article are facts given in Bourbaki, e.g. Definition 4 - A locally convex Hausdorff and barrelled space in which every bounded subset is relatively compact is called a Montel space (i.e. X Montel if and only if X barrelled + Heine-Borel; for locally convex X), Proposition 9 - The strong dual of a Montel space is a Montel space. (i.e. X Montel if and only if X^* Montel), or Corollary - The bidual of a locally convex metrizable space is a Frechet space. There's certainly unattributed overlap and dependence on earlier results. I don’t think that this isn a major concern in terms of the delete/keep discussion though, that’s moreso a cleanup point. — MarkH₂₁^talk 21:55, 16 April 2020 (UTC)[reply]

Dubious? In Bourbaki's book reflexive spaces are defined by tradition, i.e. as those for which the mapping ${\displaystyle E\to E''}$ is an isomorphism, where ${\displaystyle E'}$ and ${\displaystyle E''}$ are endowed with the strong topology (i.e. the topology of uniform convergence on bounded sets). And the results on duality are either about weak diality, or about strong duality. Not about the duality where the dual ${\displaystyle E'}$ and the bidual ${\displaystyle E''}$ spaces are endowed with the topology of uniform convergence on totally bounded sets. Which proposition in the article is contained in Bourbaki, MarkH21? Eozhik (talk) 22:41, 16 April 2020 (UTC)[reply]

The point was that some of the content, e.g. much of the "Examples" section, come directly from older sources like Bourbaki. Otherwise, you're claiming that it is entirely your original result that X is a Montel stereotype space if and only if X^* is a Montel stereotype space, or that X is a Montel stereotype space if and only if X is a barrelled and Heine-Borel stereotype space. These examples are based on the works covered in Bourbaki. — MarkH₂₁^talk 08:01, 18 April 2020 (UTC)[reply]

For Montel spaces and their strong duals the topology of unform convergence on totally bounded sets coincides with the usual strong topology on X^*, so this result becomes indeed trivial:

X is a Montel stereotype space if and only if X^* is a Montel stereotype space

I gave it for the completeness of the picture. And this is just a definition of Montel spaces:

X is a Montel stereotype space if and only if X is a barrelled and Heine-Borel stereotype space

Maybe it should be omited. Each Montel space is stereotype, and this follows from its definition and from the fact that each quasicomplete and barreled space is stereotype. This statement belongs as far as I remember, to W.C.Waterhouse. I don't know, perhaps one should mention this in the article. Eozhik (talk) 08:42, 18 April 2020 (UTC)[reply]

Montel spaces are in addition reflexive in the usual sense. So the fact that they are stereotype follows from M.F.Smith's results. One can say that she is the author. I agree that this section could be filled with more references. Eozhik (talk) 08:57, 18 April 2020 (UTC)[reply]

• Comment, as a lay person looking at the article it appears way too WP:TECHNICAL, belonging in a journal on mathematics, not an encyclopedia. Coolabahapple (talk) 03:05, 18 April 2020 (UTC)[reply]

Coolabahapple, it is normal for articles on mathematics. Look at the articles in "Encyclopedia of Mathematics", they are all technical. Eozhik (talk) 03:47, 18 April 2020 (UTC)[reply]

In what people write here I see a reasonable reproach that this article reflects mostly the point of view of a group of specialists from one country, Russia. Formally all views must be represented, including other people's understanding of what these spaces must be called. To clear my conscience, and if no one objects, I will add the term "polar reflexive space" and a link to the Köthe book. Eozhik (talk) 03:56, 18 April 2020 (UTC)[reply]

I did this. MarkH21, if you are still seeking intersections with the results of Grothendieck, this is hopeless. There are no such intersections. Our general reproach to him is exactly that he did not pay attention to the results of M.F.Smith and others, and did not understand the importance of this class of spaces which simplifies everything. Eozhik (talk) 04:21, 18 April 2020 (UTC)[reply]

The Encyclopedia of Mathematics is a technical source, moreso than Wikipedia is supposed to be.

I am not claiming that the results described in this article are due to Grothendieck, but just adding to D.Lazard's point some of the content here is based on older works not referenced here (see the comments above about the "Examples" section). As mentioned before though, it's really a cleanup issue and not the deletion argument so we shouldn't focus on it. — MarkH₂₁^talk 08:05, 18 April 2020 (UTC)[reply]

That is why the author wrote a preamble in this article. This is the usual style for such cases, MarkH21. Eozhik (talk) 05:58, 23 April 2020 (UTC)[reply]

• Keep it! This article reveals so many ways to get around the difficulties of locally convex spaces! It is tremendously useful for anyone looking at the subject and wondering, "Is there a better way?" It garners interest in a subject that would otherwise be dead (topological vector space duality) by providing a fresh perspective. I never would have discovered it by looking at the journal articles. Isn't Wikipedia all about creating community around ideas? Wham Bam Rock II (talk) 07:30, 20 April 2020 (UTC) — Note: An editor has expressed a concern that Wham Bam Rock II (talk • contribs) has been canvassed to this discussion. [reply]

• God sees everything, MarkH21. Eozhik (talk) 06:40, 21 April 2020 (UTC)[reply]
• Wham Bam Rock II, I think you should explain how you found out about this discussion because it's not good to look blankly at this picture. Even in absurdity, there must be a measure. Eozhik (talk) 06:40, 21 April 2020 (UTC)[reply]

• How else? I came to the page to look up some properties of stereotype spaces and saw that the article was about to be deleted! Wham Bam Rock II (talk) 02:18, 22 April 2020 (UTC)[reply]
• Look, if you want proof that I'm not canvassed, here's what turns up when I search "topological vector space" in my Math PDFs folder:

  

  Wham Bam Rock II (talk) 02:33, 22 April 2020 (UTC)[reply]
• Also, feel free to check my talk page. You'll see I've been a user since 2010. Wham Bam Rock II (talk) 02:33, 22 April 2020 (UTC)[reply]

• Wham Bam Rock II, thank you and excuse me for what you see here. The owners of this club forgot to put a sign on the entrance: "Anyone entering here must be ready to play a role in our absurdist theater!" Eozhik (talk) 03:15, 22 April 2020 (UTC)[reply]

• Redirect to Topological vector space per WP:PRESERVE and WP:RCHEAP. I haven't seen enough content for a standalone article. buidhe 03:26, 22 April 2020 (UTC)[reply]

  Redirect instead of delete is a good point. Reflexive space#Other types of reflexivity may be a better more specific target. — MarkH₂₁^talk 03:49, 22 April 2020 (UTC)[reply]

• Redirect per above (I change my !vote). This applies to the 3 articles under discussion. D.Lazard (talk) 09:39, 22 April 2020 (UTC)[reply]

  @D.Lazard: To which target? — MarkH₂₁^talk 13:46, 22 April 2020 (UTC)[reply]

I don't know. D.Lazard (talk) 15:11, 22 April 2020 (UTC)[reply]

If the outcome of the AfD is a redirect, then we can discuss specific targets, I suppose. (I myself prefer deletion so a discussion like that is moot.) —- Taku (talk) 00:06, 23 April 2020 (UTC)[reply]

• Redirect, with a slight preference to Reflexive space#Other types of reflexivity as the target. I don't think the case has been made that we need an entire article on this topic, let alone three. XOR'easter (talk) 01:15, 23 April 2020 (UTC)[reply]

• XOR'easter, until recently, they were two: Stereotype space and Stereotype algebra. Now they are three because for some unknown reason TakuyaMurata singled out part of the material from the article Group algebra of a locally compact group (which was called "Group algebra" before these manipulations) and created a separate article for it: Stereotype group algebra. This is a subject of separate perplexity for me because, in particular, the text describing group algebras of finite groups is no more relevant to stereotype algebras than to other group algebras. Why it must be eliminated from the article "Group algebra of a locally compact group" is a puzzle, I wrote this on the talk page. If the question of redirection is discussed now (and if by "redirection" people mean moving the text to another article), then it will be logical to move Stereotype group algebra back to Group algebra of a locally compact group. The closest article for Stereotype space is I think Reflexive space, and for Stereotype algebra —Topological algebra. At the same time, what are called "targets" here are elaborated worse than the articles that are redirected to them, I think this problem should also be discussed somehow. Eozhik (talk) 05:19, 23 April 2020 (UTC)[reply]

• I also wanted to ask people what is meant by monographs here? Eozhik (talk) 06:04, 23 April 2020 (UTC)[reply]
• Redirect or delete. The article lists ~20 non-inline references, not a single one however seems to use the article name it their title. --_{Piotr Konieczny aka Prokonsul Piotrus| reply here} 07:18, 23 April 2020 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.