In this question I forgot to add that I want the space to be sufficiently large.

One user wrote a (correct) answer pointing out a trivial example on $2$ points, answering the question.

It was my mistake to unintentionally leave out the condition that would make the problem interesting.

Question. How to proceed? Just edit the question and include the additional condition, rendering the correct (but trivial) answer obsolete? Or put the problem with the new condition into a completely new thread?

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    $\begingroup$ There are a few related threads on this meta (and many more on other metas). For example, Change a question after counter example or Altering the question in a way that makes an answer obsolete and other posts linked there. $\endgroup$ – Martin Sleziak Mar 6 '18 at 13:51
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    $\begingroup$ Probably this discussion is the closest to your question I am able to find: Questions with “accidental” trivial answers. However, it is from Mathematics Meta - which is a different site (although the overlap between the users is quite substantial). $\endgroup$ – Martin Sleziak Mar 6 '18 at 13:56
  • $\begingroup$ Thanks Martin - I guess I should delete this question in order not to clutter meta.MO, if you agree? $\endgroup$ – Dominic van der Zypen Mar 6 '18 at 14:05
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    $\begingroup$ I think a small amount of redundancy (coupled with a fresh perspective) is important. I would suggest editing to link the question to related questions. You might highlight the answer given to the earlier version, crediting it instead of dismissing it. Gerhard "Variations Upon A Mathematical Theme" Paseman, 2018.03.06. $\endgroup$ – Gerhard Paseman Mar 6 '18 at 16:30
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    $\begingroup$ Also, I would keep this meta question, and its links to the others, to make it easier for a future reader to encounter this issue and its variations. Gerhard "Changes On A Meta Level" Paseman, 2018.03.06. $\endgroup$ – Gerhard Paseman Mar 6 '18 at 16:32

Let me copy the discussion in the comments of Dominic's linked question. The pre-history of this discussion was Dominic's question posted March 6 6:02, 2018 (all times are GMT+1), followed by Francesco's answer [b], and Dominic's edit [c].

[a]: Dominic's post (abridged): A topological space is homogeneous if (...). Does there a homogeneous Hausdorff topological space (...) for which every continuous self-map is either a self-homeomorphism or constant? March 6 6:02

[b]: Answer posted by Francesco Polizzi (in its original form): Take the discrete space with two points. It is clearly homogeneous and Hausdorff, and its only self-maps are the two constant maps, the identity and the involution exchanging the two points. - answered Mar 6 at 8:55 Francesco Polizzi.

[c]: Edit by Dominic of the question Mar 6 at 10:19, adding the assumption that the space is infinite and then after the comment [d] below: "EDIT. I forgot to add "infinite" in the original question." edited Mar 6 at 10:33

(the next steps are comments to the question)

[d] Well, you should not change the question once there is already an answer. In this way a perfectly correct answer becomes a wrong one. Please write an edit, explaining the modifications you made. – Francesco Polizzi Mar 6 at 10:25

[e] I disagree with you. Even if this corresponds to the original formulation, this does not deserve an answer, but rather an comment saying that the question should be reformulated. If this were the intended question, it would be closed as off-topic. – YCor Mar 6 at 13:06

[f] @YCor: of course you can disagree. At any rate, this was the question, it was unanswered, open for more than one hour and it also had un upvote. Sometimes it happens in life that people miss trivial counterexamples, this is not my fault. – Francesco Polizzi Mar 6 at 13:21

[g] That said, I still think that modifying a question with an answer, making a right answer a wrong one is a bad practice, regardless if someone finds such an answer interesting or not. – Francesco Polizzi Mar 6 at 13:22

Now let me comment further. I think (1) it's bad practice to modify a question after it's been replied, because it's a lack of respect towards the person who did the answer, who possibly did some efforts to handle the question. In a sense, it reflects that the OP does not consider the efforts made by the person who wrote the answer as worthwhile.

But it turns out that this judgement can be appropriate, when the answer consists of a trivial counterexample or just a link. (In my own experience, a case with possibly a little effort by the replier, and where the question was subsequently modified, is this answer.)

Next, I think and it's been discussed at many places, that (2) it's bad practice to post trivial answers to trivial questions (one reason among other being that it forbids the OP to delete the question; one other being to discourage homework questions - anyway it's not the point here). If a question has a trivial answer, it should be closed, and the trivial answer should be mentioned in the comments. If one can give to the OP the benefit of the doubt that there's a missing hypothesis, then it's better post a comment addressing this, rather than immediately voting to close.

If we had followed Francesco's request ([d] above) in the current case, what would have happened would be:

  • a new post would have been done with the question excluding finite spaces
  • As regards the original post, Francesco's answer would have been accepted, while the post would have been closed as off-topic.

Sometimes an interesting question is spoiled because the poster forgets an important detail, or explains it ambiguously. Sometimes there is no mistake, but it simply happens that the first answers or comments make it clear that the truly interesting question is just a bit different. What it usually happens, and I find perfectly correct, is that the poster apologizes in comments, and decides, maybe after suggestions by other users, whether it is worth posting a new modified question, with a link to the previous one, or just making an edit (complete with date and explanations) in order to update the original question. Both ways are good to me; which is more convenient, really depends on the case. Of course, I agree with Francesco that changing the question without any explanation and without leaving any trace does not add to the clarity, even when there is absolutely no bad intention, like in the present case. Talking to my personal experience, let me add that sometimes I know in advance that a poster (especially newcomers) will mix up the question, and I copy their exact words in my answer, as a precaution. Also, sometimes the first wrongly stated question actually helped (and forced) me to understand better the right answer to the successive right question.

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    $\begingroup$ In a very recent post (mathoverflow.net/questions/294779), some discussion led the poster to change his question in a way that I could give an answer (in this case, something non-trivial but very classical). Still I had a serious doubt whether this was the intended question and whether once answered he wouldn't change the question. So I double checked, posting a comment. I got confirmation and posted a detailed answer. $\endgroup$ – YCor Mar 12 '18 at 20:32

In my opinion the best way to handle this is usually to accept the trivial answer and ask a new version question containing the correction. My arguments:

  • If you didn't think of the trivial example then it's likely that other people won't either. A unique service that MO provides is that you can google trivial questions and see trivial answers, whereas such trivialities are usually filtered out of published papers and textbooks. This has saved me a lot of time and pain in the past.

  • Noticing simple examples often requires a lot of serious intuition and expertise in a subject, so it's generally not the case that the answerer is getting undeserved reputation.

The main reason to modify the question instead of accepting the trivial answer is to avoid polluting your question list with what turned out to be a slightly silly question. But taking that hit carries significant possible upsides for others.

Of course my arguments don't apply if the error is so trivial that it requires no real expertise to spot it - e.g. forgetting to exclude zero in a nontrivial question about prime factorizations. Those issues should be settled in the comments. But I could see a reasonable person (myself included) spending a bunch of time trying to prove the statement in your original question before running into the two point counter-example, so I would have kept it around for posterity and asked a new question.

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    $\begingroup$ Your point about not thinking of the trivial example is very good - thanks for your post! $\endgroup$ – Dominic van der Zypen Mar 23 '18 at 7:27
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    $\begingroup$ Basically I agree with your arguments but I don't see any reason they support your conclusion; they could even support the opposite conclusion. When I read a question, I sort of trust the OP (esp. if not a new anonymous user) to have thought enough to discard too trivial counterexamples; if I unsuccessfully think about the question and then see it as settled because of a trivial degenerate example, I'd get even more frustrated. $\endgroup$ – YCor Mar 24 '18 at 7:54
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    $\begingroup$ @YCor One legitimate way to use MO is to ask about things outside of one's direct area of expertise that come up in research, and I suppose my argument applies best to these sorts of questions. For instance it's not hard to imagine a geometer encountering a statement in homological algebra which is reasonable for coherent sheaves but fails if you view $\mathbb{Q}$ as a $\mathbb{Z}$-module or something (I don't have a specific example in mind). It can be hard to get up to speed on the standard examples in the new area, and MO can be a good resource for others making the same journey later. $\endgroup$ – Paul Siegel Mar 24 '18 at 8:48
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    $\begingroup$ Do you consider the discrete topological space with two elements as a "standard example in the new area" (to which it can be hard to get to a non-specialist in topology)? $\endgroup$ – YCor Mar 24 '18 at 8:50
  • $\begingroup$ @YCor I don't know the backstory for that question specifically, but I could envision someone working primarily on Riemannian homogeneous spaces trying to make an argument work more generally and running into the OP's question along the way. Such a person would not be particularly primed to consider two point spaces (though would probably feel silly in hindsight). I suppose this discussion underscores the value of adding some motivation to a question. $\endgroup$ – Paul Siegel Mar 24 '18 at 8:58
  • $\begingroup$ Yes. we boil down to the question about what should be considered as trivial, which is of course subjective, but at least boils down to a standard subjective question for users of this site: which posts are suitable, which ones should be closed. One can think in this way before answering something potentially too trivial (for the replier) or before changing a question after a "too trivial/ unexpected" answer (for the OP). Namely, an answer is "too trivial" if it makes the question, literally interpreted so as to make the answer acceptable, prone to be closed as off-topic. $\endgroup$ – YCor Mar 24 '18 at 9:06

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