Isn't this just a form of gatekeeping, where you only get to ask a question about mathematics if you've already learnt enough of mathematics to rigorously formulate your problem?
This question seems to be built on some rather binary thinking: either (the question asserts) a question remains open and the asker is helped when people post answers, or the question is closed and the asker is never helped at all.
The reality is much more nuanced.
Math SE serves many goals. Two of these are (a) helping an individual asker at the moment that they ask a question and (b) helping future askers by building a repository of questions and answers. I would argue that poorly presented, confusing (and confused) questions do a great deal to hinder (b), and that (a) can often best be served in such situations by addressing an asker's concerns in the comments.
In other words, we often help askers in the comments while simultaneously closing (and ultimately deleting) their questions. Someone can get the help they need while also having their question closed.
How can we expect to help users who have legitimate questions, but not the mathematical maturity to formulate their question perfectly, if we keep closing their questions for lack of mathematical maturity?
- We can use the comments to suggest ways in which they can clarify their question.
- We can help users to turn those comments into answers.
- We can reassure new users that closure is not the end of the world, and that closing a question only means that they need to take some time to improve the question.
- We can stop immediately answering confused and muddled questions until they are clarified (my impression is that much of the rush-to-close is motivated by the fact that there is a rush-to-answer, and that answered questions are only very rarely improved---if answerers would spend more time helping askers in the comments before answering, I suspect that a lot of potential close voters would be slower to cast votes).
Frankly, I think that it is incredibly paternalistic to suggest that someone with a legitimate question should just be handed an answer because they lack the maturity to formulate that question properly. If we are really interested in teaching, then perhaps we should be using the comments to help askers to formulate their question better, and then posting answers?
In the case of If we put the empty set into a function why do we get the empty set back?, I think that we can all agree that the asker is confused. However, the asker must have been motivated to ask that question for some reason. Presumably, they are a student in some class, and they have lecture notes or a text in which it was presented that $f(\varnothing) = \varnothing$. The asker should provide that context.
Somewhere else in that text, there should be a definition of what the notation $f(A)$ means, when $A$ is a set. There are a number of comments below the question in which this definition is asked for (in one way or another). If the asker could explain what they mean, someone else (or the asker) could easily edit that into the question.
Another commenter asks "What does it mean to multiply a set by $6$?", and the asker seems at a loss to even understand why that question matters. This gives the impression that the question is so far over the asker's head that they need to take a step back and ask some more elementary question before trying to tackle the image of the empty set (that is, this is an XY Problem).
The question itself is extremely muddled and unclear, and it is not at all obvious how one might reasonably solve the asker's problem.[1] A number of people have requested clarification in the comments, and the close banner at the top of the post provides a link to this answer, which suggests adding motivation and / or a source.
The asker has been given the resources to improve their question—if they want their question reopened, they have been given a lot of good advice. If, on the other hand, they are satisfied that they have an answer, then I see no compelling reason to reopen the question, as I have difficulty seeing how, in its current form, it is likely to be useful to a future asker.
Finally, for what it is worth, the question is a duplicate many times over. For example:
Even if this particular asker's question is deleted, the answer given to the question under discussion largely duplicate answers already provided to other questions.
Regarding Order and isomorphism exercises Charles C. Pinter, (a) Math SE is not a homework proofreading service, (b) questions should be narrow and focused (that question seems to be asking about two distinct exercises), and (c) further context is required.
Regarding (a), while there is a solution-verification tag, the tag wiki makes it clear that these kinds of questions should focus on the specific concerns of the asker. "Is my proof right?" is not a good question. This is further articulated in Best way of asking "check my proof" questions.
It also bears mentioning that the asker did not use the solution-verification tag, which seems to indicate that they are not even aware that it exists. (I added the tag after being made aware of the question in this meta post).
Regarding (b), that question should be at least two different questions (one for each exercise.
Regarding (c), I left a comment there indicating possible avenues for improvement.
[1] For what it is worth, I think that both answers completely fail to address what I think the underlying problem is, i.e. that the asker doesn't even understand what a function is, let along how an function might act on a set (or what the image of a set under a function is). But the question is so muddled that I can't be certain that this is the underlying issue.
The fact that I diagnose the problem very differently from those who decided to answer the question indicates (to me, at least) that the question is so muddled and the underlying issue so unclear that we really need to wait for the asker to give more input before committing answers to the repository.
Context, in the form of definitions and/or a citation to a text, would likely clarify this immensely.
