When might it be reasonable that a question is closed as offtopic because it "does not appear to be researchlevel mathematics" while one of many narrow special cases of that question, posted separately, gets 7 upvotes and its only posted answer gets 13?

9$\begingroup$ Could you be more precise regarding what you are talking about? It seems it is something specific not a thoughtexperiment. (But I can imagine it being reasonable; that the one is closed and the other not.) $\endgroup$– user9072Commented Jul 26, 2013 at 20:45

$\begingroup$ I think I know what it is about, now. Still it might make sense to be more specific. $\endgroup$– user9072Commented Jul 26, 2013 at 20:58

4$\begingroup$ @quid and Michael: Would it be possible for one of you to share an example? Or would that be inappropriate somehow? $\endgroup$– Ricardo AndradeCommented Jul 26, 2013 at 22:09

1$\begingroup$ Why is this question getting buried so fast? $\endgroup$– Ricardo AndradeCommented Jul 26, 2013 at 23:01

$\begingroup$ I hesitate to cite an example, since whenever I do that here on meta, lots of people want to change the subject and argue about the topic of any cited postings. Yes, it's possible. It happened. $\endgroup$– Michael HardyCommented Jul 26, 2013 at 23:03

3$\begingroup$ @RicardoAndrade: for the specific one I then thought was meant see Michael Hardy's comment on S. Carnahan's answer. For the abstract situation, the example of S. Carnahan expresses better than I could what I had mainly in mind. $\endgroup$– user9072Commented Jul 26, 2013 at 23:46
1 Answer
I can't provide a characterization of such situations, but it is not hard to come up with new ones. For example, a question like "What can you say about algebraic curves with nodes?" would be rightly closed, while a wellwritten question about the existence of a plane curve of a certain degree and a certain number of nodes may be wellreceived.
In general, it helps if the question appears to have had a substantial amount of focused mathematical thought behind it.
Edit: In response to comments, let me refine my example. If someone asked the question "What do nodal algebraic curves generally look like?" together with the text "I sketched the graph of $y^2 = x^3 + x^2$ and was startled to find it looking like a fish." it would be rightly closed.
Regarding the specific situation, it looks like Neil Strickland's comment answered your question (inasmuch as it could be answered) in two sentences. Your later question was substantially better than the first one. In particular, because you were seeking a specific characterization, it was an actual mathematical question, not just a special case of the first question.
If someone is calling you names on MathOverflow, we moderators would be interested in hearing about it. On the other hand, if there was a heated email exchange out of the public eye, I don't think it is reasonable to bring it up here.

1$\begingroup$ This question is a narrow special case of this question. The narrow special case currently has seven upvotes and a posted answer has 13. The more general question was closed as not researchlevel mathematics. Conceivably this could be viewed as similar to the hyphothetical, but one of those voting to close said it's a highschoollevel question. Now everybody figure out what graphs of some such.... $\endgroup$ Commented Jul 26, 2013 at 23:27

1$\begingroup$ ....functions look like when they were in high school (including me, in ninth grade). They also learned about natural numbers $1,2,3,\ldots$ in kindergarten. Therefore the theory of the natural numbers is kindergartenlevel stuff. In ninth grade I quickly figured out what the graph of the tangent function looks like, and I remain far from convinced that mathematicians understand that graph's geometry. I will soon attempt to publish a result about that. That a referee might say it was done 50 or 250 years ago (the latter by Euler?) is of course possible. $\endgroup$ Commented Jul 26, 2013 at 23:30

1$\begingroup$ In individual instances one can find the gross shape of such graphs by methods that are easily and quickly applied by highschool students, but that doesn't mean that results about the relationship between the form of the function and the properties of its graph are highschoollevel stuff, nor that they are so easily obtained. The person who said it's highschoollevel stuff also told me I'm either an idiot or begin wilfully obtuse if I hesitate to agree with that. $\endgroup$ Commented Jul 26, 2013 at 23:33

9$\begingroup$ @MichaelHardy you present this situation more drastically then it was, as far as I can oversee. With negative effects for you and others. Maybe or not your original question was received harsher than it deserved. Maybe or not your original question was not well written. But good for everbody the second try worked a lot better. I'd say, let us move on. $\endgroup$– user9072Commented Jul 27, 2013 at 0:45