7:03 AM
In any case, many questions about Baire space that we have on this site at the moment are probably tagged (descriptive-set-theory).
7:18 AM
Maybe I should have phrase it like this: Should (the-baire-space) be a subtag of (descriptive-set-theory)?
I have first encountered this space in connection with DST. And despite the fact that it is metric (metrizable) space and we can speak about it just considering the metric structure/topological structure; in my mind it is still closely connected to DST.
@MartinSleziak I noticed a couple edits from you, and was certain I'd find some new content here. You're pretty predictable that way. ;-)
@MartinSleziak Here are my thoughts. The d-s-t tag should be used for questions really about descriptive set theory: definability (Borel, projective, etc.) of subsets, uniformazation, separation theorems, etc. While the Baire space is central to d-s-t, not every question about it is really a question of d-s-t. That it is not sigma-compact is a purely topological property of the space, and doesn't really figure directly into d-s-t, as I (probably mis-)understand it.
Based on what you wrote, probably none of the 4 questions currently tagged the-baire-space should have descriptive-set-theory tag.
Stone-Cech compactification is studied in topology. If we had (stone-cech-compactification) tag it would not be unreasonable to expect that every question having this tag would also have (general-topology) tag.
But I can imagine question about $\beta\omega$, which is mostly about semigroup structure or about some properties of ultrafilters, where topological properties would not play a big role.
If the Baire space is almost exclusively studied in descriptive set theory, then the situation is similar.
To be more precise, the correlation between baire-space and descriptive-set-theory is much weaker than the correlation between stone-cech-compactification and general-topology.
So basically I have no objections against your assessment. But I thought that it is good that it was discussed at least for a bit.
As I have mentioned, many questions about the Baire space are currently under (descriptive-set-theory) tag: math.stackexchange.com/…
So if we are going to retag at least some of them, we can also have a look whether d-s-t tag should be removed or not.
I have removed descriptive-set-theory from some question tagged the-baire-space (and also added metric-spaces in some cases.)
7:39 AM
We will see what happens with the-baire-space. In any case, if I see new questions I will use this tag. And I will try to retag a few older ones from time to time.
7:43 AM
Just for the record (and so you have something to link to when the time comes), I decided to create this tag because that space is used under so many different names/descriptions that it is virtually impossible to find duplicates. Add to this that searching for MathJax is terrible on this site, and there's probably an entire corpus of questions/answers that no-one can find.
We have some questions about Polish spaces, but it is probably better to use descriptive-set-theory than to create a separate tag.
Thanks for your explanation of the reasons for creating the new tag. (As you say, it might be useful ot have something to link to in case this is discussed. And perhaps also for discussions about some similar tags.)
Although there is also an older discussion in connection with [tag;sorgenfrey-line], where you have mentioned something similar.
Some thoughts on what makes tag useful
Oct 9 '14 at 11:44, 20 hours 44 minutes total – 33 messages, 2 users, 0 stars
Bookmarked Oct 22 '14 at 12:11 by Martin Sleziak
8:12 AM
Only now I've noticed that the explanation when to use descriptive-set-theory together with the-baire-space is given in the tag-wiki.
3 hours later…
11:37 AM
Would convergence-tests tag for questions about convergence tests be useful? Perhaps as a subtag of sequences-and-series.
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