I was wondering if there should be a distinction between elementary topology and, say, set-theoretic topology similar in spirit as elementary-set-theory and set-theory. At the moment completely trivial things are mixed with much more advanced concepts under general-topology.

Interesting idea, but I am not sure whether there would be easy way to make a distinction between the two.

Perhaps elementary-topology would contain, roughly said, the stuff from topology which is often mentioned in the courses in analysis, usually in the context of Euclidean spaces or metric spaces?

Here is some older discussion from meta; Sophistication level tags?

@Martin Since general-topology is one of the most frequently used tags, it would be good to discuss this at meta first, so that we hear opinion of more MSE users.

(Of course, it is also possible that some people notice your post here and will reply here; but there are not many people who visit this chatroom frequently.)

So if you feel strongly about this idea (or if you want to get more relevant feedback), posting a question on meta would be the best thing to do.

@MartinSleziak I was thinking that roughly the first five chapters of Munkres would be "elementary", that is, things covered in a typical one-semester introductory topology course: continuity, separation axioms, compactness, connectedness and basic countability axioms (first and second countability, Lindelöf, separability), Urysohn and Tietze's theorems. Notions such as paracompactness, nets and filters and metrization theorems would probably be borderline.

As would be Tychonov's theorem. On the other hand, I would say cardinal invariants, properties of the Stone-Cech compactification beyond the definition, topologies on function spaces, and so on would belong to the more advanced section.

I will think about it a bit more and see if I get some more reactions here before I post on meta. Thanks for your feedback!

@Martin The questions what to do with the question already tagged as general-topology will probably come up. It would be a lot of work to go through 5k questions and check, which of them should be retagged. (And this only can be done by few questions at once, so that the front page is not overfilled by the questions bumped in this process.)

The largest retagging I have seen here was the removal of algebra tag - there are several discussions about this on meta. When I joined the effort, the tag had about 700 questions and it still took quite a long time.