7:23 AM
@MartinSleziak Just let me say a few words. First of all, most of our tags are not consistently applied to questions. I personally really don't know when the or tags are appropriate, for example. And I'm sure I'm not alone in this, and so they are unevenly applied to questions . This in turn makes them almost useless as far as filtering is concerned.
Though I don't have any real data, I would surmise that most of our tags on the same conceptual level have similar problems. They are about a mathematical concept whose scope is ill-defined, and so the tags don't get used consistently. (Some of our area-tags have a similar problem, but I think the inconsistency of using or for questions about, for example, the openness of specific sets of reals is due to other external factors.)
I have a hypothesis that our best tags are either extremely broad area tags, or very narrow tags about a specific mathematical object/method.
Note that I'm certainly not judging the usefulness of a tag solely on the number of questions that use it (or could use it), but rather how it is put to use in practice.

7:43 AM
@ArthurFischer I am responsible (at least partially) for the creation of tag. I use it on all questions where compact sets/spaces appear (unless they play only tangential role).
I think that this is in agreement with the tag-excerpt: The compactness tag is for questions about compactness and its many variants (e.g. sequential compactness, countable compactness) as well locally compact spaces; compactifications (e.g. one-point, Stone-Čech) and other topics closely related to compactness.
@ArthurFischer I certainly agree that is used quite consistently. I am not that entirely sure about . I think there are some questions which I would rather see as . I don't think questions should be under (real-analysis), but I think I saw such questions.
There was also some discussion on meta about using real analysis tags‌​. Willie Wong's answer mentions the fact that various people have various definitions of what real analysis is.
But I certainly agree that "big tags" are used quite well. One reason is that they often define some area of mathematics. Another reason might be that, having seen many questions with those tags, users learned how to used them by example.
I certainly agree that I do not know when to use .

7:59 AM
@MartinSleziak But where is this line drawn? Countable compactness is specifically mentioned, but what about paracompactness? Lindelöfness? metalindelöfness? Do all questions about $\beta\omega$ fit under this tag?
Please don't think I'm attacking you for creating this tag (I had no idea), but I think it is an example of the "mushy middle" that I mentioned on meta. And I also think there are at least dozens of these kinds of tags.

8:11 AM
@MartinSleziak I agree that most users get these huge area-tags mostly right because they do correspond to big areas of math, and often these questions come from a course or a text whose title includes the name of that area. That makes it often quite easy. I also think that the opposite end, the very focused tags, can be very useful. (I've been thinking about adding and tags -- as synonyms -- since this construction comes up often enough.)

@ArthurFischer My intention was the it should include the questions about compactifications (of any kind). So I would probably include it in questions about $\beta\omega$.
If not for any other reason is that it helps searching, since $\beta\omega$ is also denoted $\beta\mathbb N$, someone might denote id $\beta D$ and say that $D$ is a discrete countable set. It is much easier to search in the tag than trying various possibilities; there are some posts about $\beta\omega$ which do not use the name Stone-Čech compactification.
About paracompact and Linfelöff I would say maybe. I am not sure - and it is not specified in the tag-info....
But I agree that it is a good example of a tag where we can find questions where it is rather unclear whether some questions belong there or not.
I am not sure about , isn't it too specific. But as you say, it appeared many time.
I had also some doubts about , but the tag was rather big when I first noticed it.
Sep 11 at 11:11, by Martin Sleziak
If we have tags (and ), I would expect to have also . At least to me the notion of quotient group seems at least so important (and potentially useful as a tags) as the notion of normal subgroup.
Sep 11 at 11:12, by Martin Sleziak
Perhaps it would make sense to have quotient groups and normal subgroiups in the same tag. (A synonym, maybe?)
But it seems that I digressed to specific tags from your general point describing what kind of tags you see as somewhat problematic.

8:27 AM
@MartinSleziak The problem is that the space is often described in questions in different ways. As "Sogenfrey line" as "lower-limit topology" or simply describing the basis. This makes searching for questions about the space difficult. It is also pretty clear whether a question is about the Sorgenfrey line. (I think it's a bit funny that we don't balk at the tag, but others are too specific.)

I agree, that if this helps searching (because many different names are used), then the tag will be useful.