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I recently asked two questions: Simultaneous coset spaces and Manifolds as simultaneous coset spaces which appear to be quite similar. The first was closed as 'not research-level mathematics' while the second was not. I assume this means that the first question is too trivial for this site and the second one is not (or has not yet been identified as such).

I am a research mathematician and both questions arose during my research, so both questions meet following help centre criteria:

  • the sorts of questions you come across when you're writing or reading articles or graduate level books (I did)
  • your question is of interest to at least one other mathematician (it is trivial and therefore has been solved by another mathematician).
  • questions that actually have a specific answer

I suspect that something else is meant by 'not research-level' in this case. It seems it could be any of the following:

  • There are some mathematicians on this site who know the answer already.
  • The answer would be obvious to all mathematicians working in the area (I do not work in this field and it arose in a different context).
  • A mathematician working in any area would know the answer (I don't believe this is the case).

Could somebody explain which (if any) of these is the correct reason?

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    $\begingroup$ Were you not satisfied with the answer YCor gave in a comment? If what YCor wrote is correct, then it would seem that the question did not rise to research-level. $\endgroup$ – Gerry Myerson Dec 22 '15 at 15:01
  • $\begingroup$ I'm happy with the answer YCor gave. I just wanted to know for future questions why this one was not on topic. $\endgroup$ – octopus Dec 22 '15 at 15:30
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    $\begingroup$ Concerning the specific questions you asked, sets are easy to tackle because the only invariant of sets is cardinal. So one only has to consider the possible cardinals of the two quotients of the group acting. I guess that question was closed because it was expected that this principle belongs to the common core shared by mathematicians; it may not be the case, but could be somewhat expected. On the other hand, the question about continuous action on manifold is much more subtle, since the object involved have more structure (and thus less isomorphisms, and thus more diversity). $\endgroup$ – Benoît Kloeckner Dec 28 '15 at 13:06
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"Not research-level" is not a well-defined phrase, and there is wide variance among users as to what it means. But it might mean here that the users who voted to close thought it was too easy to take seriously, or that you didn't think about it too hard, or something like that.

While it is my belief that the general trend towards toward closure is pretty strict and hard-nosed, and that not a few snap judgments take place (we are all human), the question poster can go some distance to counteract this tendency by providing motivation and context for the question. This helps give the impression that the poster actually is engaged in serious research (even if the answer is easy or dead obvious to at least one person at this site), and so people who are active in reviewing questions might be more 'forgiving' than they would otherwise.

The original idea of this site is that questions that stump one researcher might be (sometimes easily) dispatched by another, and that ethos is still alive and important here, but the standards have become stricter over the years. But don't be discouraged; to repeat, just remember that it helps to add context and/or motivation (this is discussed more at the 'help' center).

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    $\begingroup$ Here is my anecdote: I once posted a question and received two down votes within the first hour as being " not research level" .so decided to delete it. But after a few hours changed my mind and asked the very same question, worded slightly different. I received 4 up votes and sure enough people thought the question on was worthy ,whatever that it means... $\endgroup$ – BigM Dec 22 '15 at 17:25
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    $\begingroup$ @S.Zoalroshd: The wording can certainly make a difference. -- If a question is written down in a sloppy way, it may be downvoted and closed, while if the same question is formulated well, the community may welcome it. -- I'd say this is in no way a problem, but rather a "feature" of this site. $\endgroup$ – Stefan Kohl Dec 22 '15 at 17:47
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    $\begingroup$ It is of course exactly the opposite. In most cases, people who don't understand a question really don't understand the question, period, and obviously it is not for them. I have observed that (perhaps non) mathematicians in MO tend to think that they can comment on everything (they can, but they obviously should not). $\endgroup$ – John B Dec 23 '15 at 1:16
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    $\begingroup$ @JohnB a question on this site is ideally written in such a way that it is accessible to a trained mathematician irrespective of specialization. In particular, it will give enough context so that one can easily look up missing definitions, terminology etc. This is perhaps not always possible, but most of the time it is possible. Somewhere you said recently: "As always, questions are formulated for the expert." This is just not what is to be done on this site. Of course, formulating for the expert may be easier but one is expected to do the extra work of formulating in an accessible way here. $\endgroup$ – user9072 Dec 23 '15 at 9:59
  • $\begingroup$ @quid, It is of course all the opposite of what you say, but it is already detailed above why. $\endgroup$ – John B Dec 23 '15 at 10:23
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    $\begingroup$ There are various benefits to making posts more accessible. For example, I saw an abstract recently that mentioned new results obtained using discrete admissibility in analyzing certain dynamical systems, and was thinking of posting something to your question on the matter, so that you could contact the experts directly about it. However the question is gone, so I guess you are no longer interested. If the question had been made more accessible, you and others might have gotten some use out of it. Gerhard "Off To Help Someone Else" Paseman, 2015.12.23 $\endgroup$ – Gerhard Paseman Dec 24 '15 at 7:44
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    $\begingroup$ I see now it has moved off of some of the listings, but is not gone. I will see about posting the abstract for you. Gerhard "Not Yet Gone Or Forgotten" Paseman, 2015.12.23 $\endgroup$ – Gerhard Paseman Dec 24 '15 at 7:56
  • $\begingroup$ One thing that can often help with borderline cases: ask first on math.stackexchange, and if you don’t get an answer there that meets your needs, re-ask here and say so (with a link to the math.se question). I for one find a lack of answers on math.se a fairly convincing argument that a question is high-enough level to justify being on MathOverflow (providing the question is well-written and so on, of course). $\endgroup$ – Peter LeFanu Lumsdaine Dec 26 '15 at 12:48
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    $\begingroup$ @PeterLeFanuLumsdaine That's commonly done, but I often find that the question winds up not being all that suitable for MO (and so I don't agree it's a fairly convincing argument). I think a problem with math.se is that it's swamped with questions, and many questions fail to elicit an answer because they don't excite anyone, or they are not sufficiently low-hanging fruit, or something else. $\endgroup$ – Todd Trimble Dec 26 '15 at 13:32
  • $\begingroup$ @ToddTrimble: yes, that’s true. But it means that anyone reluctant to answer it here as “not research-level” has a fallback option of answering it there instead. $\endgroup$ – Peter LeFanu Lumsdaine Dec 26 '15 at 22:43
  • $\begingroup$ @PeterLeFanuLumsdaine Good point, and "nothing ventured, nothing gained" as they say. $\endgroup$ – Todd Trimble Dec 27 '15 at 0:57

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