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This post is about the question Is it meaningful to work on convergencies, integration, etc. on the Zariski topology? It is an interesting, relevant question which attracted two excellent answers. The question is slightly ambiguous, but in a way where it is easy to understand what the author is thinking, and the answers do an excellent job of addressing this ambiguity.

Added later: the question got reopened.

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    $\begingroup$ I am not at all enthusiastic about this question, and I think it was right to close it as being unclear (to me it is unclear). To me the answers don't exactly clarify the question; they are somewhat artful ways of talking about things that could be of interest to the OP, much in the way that a kind and skilled professor might address a confused or ineptly formulated question, making the best of a situation. (Incidentally, we have this thread for reopen requests: meta.mathoverflow.net/questions/223/requests-for-reopen-votes.) $\endgroup$ – Todd Trimble Apr 20 '14 at 13:47
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    $\begingroup$ To me this question resembles the kind of discussions that I enjoyed as a grad student, both as asker and answerer, with other grad students in different specialties. Personally, when I am unsure how to best formulate a question, I especially appreciate an opportunity to ask it. If this type of question is unwelcome on MO, I would personally regard this as a loss, although I gather that my opinion is in the minority. $\endgroup$ – Frank Thorne Apr 20 '14 at 16:27
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    $\begingroup$ Well, the community should continue to have discussions about MO norms, and there are not a few who think the prevailing norms are too strict. My comment should be interpreted less as coming from an MO "cop" and more just a personal statement that I indeed found the question unclear; particularly that I don't get what OP meant by <<the Zariski topology is meaningful as being a "topology", rather than being a set which sufficies the axioms of being a topology. Is there a understandable example which views the Zariski topology as a "topology">> Did OP obliquely mean a Grothendieck topology?? $\endgroup$ – Todd Trimble Apr 20 '14 at 16:56
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    $\begingroup$ I took "topology" (in quotes) to mean the sort of thing that one sees in elementary topology --- convergence, continuity, connectedness, and the like. The answers made it clear that such things are not to be expected from the Zariski topology, which I think answers that part of the question (if I understood it correctly). $\endgroup$ – Andreas Blass Apr 20 '14 at 21:26
  • $\begingroup$ @AndreasBlass But he says 'a "topology"' (my emphasis), not "topology" as a kind of collective noun. Anyway, I asked what was meant at MO main, and maybe OP will pop by to clear it up. $\endgroup$ – Todd Trimble Apr 20 '14 at 21:48
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    $\begingroup$ When I've read the question it immediately translated in my mind as "Topology is for talking about converging sequences: what the heck is the Zariski topology about?". Probably I got a bit carried away in my willingness to reply that there's more to geometry than converging sequences. That said I think that the question may use a clarification $\endgroup$ – Denis Nardin Apr 21 '14 at 3:49
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    $\begingroup$ Technically, this question is not "closed", it is merely "on hold". This means it can be re-opened provided it is re-worded to make it acceptable. $\endgroup$ – Gerald Edgar Apr 21 '14 at 12:26
  • $\begingroup$ @GeraldEdgar I think you make a good point, but still I cannot help but point out that even if it were technically closed it could also be re-opened. $\endgroup$ – user9072 Apr 22 '14 at 15:56
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There are two ways of interpreting your question. Literally, you seem to be asking for an explanation from those who voted to close the question. I was one of them, and the question was genuinely unclear to me. When I voted, I don't think there were any answers; but I am not sure if the answers (nice as they are) would have changed how I felt about the question.

But probably the spirit of your question is to ask for it to be reopened. This is certainly reasonable, but I don't feel persuaded to cast a vote to reopen. I think the question could be improved by someone (e.g. OP or you or ...) who feels they understand the spirit of it and is willing to edit it.

Finally, I posted this comment on main: there is a closely related question on MSE which I think is posed more clearly, and has a very nice answer by Matt E(merton). See https://math.stackexchange.com/questions/53852/is-there-a-way-of-working-with-the-zariski-topology-in-terms-of-convergence-limi/53912#53912

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  • $\begingroup$ Please note that I was advocating on behalf of someone else's question -- I do agree that the question left room for improvement. Also, I agree that the question was very nicely posed and answered in the MSE link you mentioned! $\endgroup$ – Frank Thorne Apr 22 '14 at 1:18
  • $\begingroup$ @FrankThorne: I appreciate your point, which as I mentioned above is eminently reasonable. $\endgroup$ – Lucia Apr 22 '14 at 1:55

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