I just stumbled upon a question: What is a Limit?
But I was surprised that it wasn't closed for too broad, it was upvoted! Can I ask what is topology? And the comments are also not responded to by the OP. Still it is upvoted? I know there are $-11$ downvotes on it also, but the ratio of Upvoters to downvoters is quite big, $21:11$. Is it fair?

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    $\begingroup$ Note that the question was asked in 2010, in the early days of the site. Standards were much laxer then. In fact, that question was asked when math.SE was still in private beta (cf. History of math.SE), so my guess is that it's a question that was asked just to fill up the site with some content when it was still super-new. $\endgroup$ Oct 6 '15 at 13:58
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    $\begingroup$ The question you link to is over five years old. Whichever way it was voted back in the day does not reflect the way users might feel about such questions today. About your last question - very few things about voting are fair. $\endgroup$ Oct 6 '15 at 13:58
  • $\begingroup$ Concluding, can I ask: "What is topology" instead of asking "Please recommend me a book for topology"? $\endgroup$ Oct 6 '15 at 14:01
  • $\begingroup$ You certainly can, but if I were you I wouldn't expect the question to stay open for long or to get good answers. $\endgroup$ Oct 6 '15 at 14:04
  • $\begingroup$ This seems related: What's the policy on “what is X?” questions? and Are “What is X?” questions acceptable?. (However, as the comments above said, things may have changed in the meantime.) $\endgroup$ Oct 6 '15 at 14:30
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    $\begingroup$ I just noticed, that question is in fact the second question ever asked on the website (look at the post id in the URL; the first is this one). Needless to say, standards have evolved since then...! $\endgroup$ Oct 6 '15 at 15:26

The issue with the question "What is a limit?" is not so much that it is "too broad" but rather that it lacks some context and details. Although, it is not that bad as the OP had mentioned calculus books. Thus, the question could reasonably be answered by explaining what the notion of limit is about (in a calculus context). This is not a good question but not that unreasonably broad either.

The question you propose is quite different, as it asks about a subject-area and not a mathematical notion. A question that would be similar would be "What is a topology?" (perhaps this is the one you had in mind).

Just like with the original question just this is as a question not quite precise enough. However, both the following variants might in fact work:

  • What is a topology? I read in my analysis-text that the concept of continuity and related notions can be generalized from functions defined on a metric space to more general spaces by considering sets equipped with a topology. I would like to know: What is a topology?

  • What is a topology? I just read the definition of topological space. I can follow the definition on a line-by-line basis, but I have no idea how this could be useful or why the definition is as it is. I would like to know: What is a topology?

The two questions are quite different. The former asks about the technical definition (not knowing it) while the latter asks about the intuition behind the concept. I cannot see anything inherently wrong with either of the two questions, except that the first likely could be answered by a search and thus might not qualify and the latter could be phrased more concisely.

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    $\begingroup$ What is topology? I read that a topologist can't tell the difference between a donut and a coffee cup. But when I look for "topology" on Wikipedia, it's all about arbitrary unions and things like that. So, what is topology? $\endgroup$
    – GEdgar
    Oct 6 '15 at 17:26

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