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The tag currently used for point-free topology (aka “pointless” topology) is “”. I think the name is a bit restrictive: while writing this question (which, indeed, does not contain the word “locale”, but frames and locales are just opposite categories to one another, and the question could be couched in the language of locales and sublocales), I missed it, and I think it's not the first time this has happened.

I believe one or several of the following would be more appropriate:

  • “frames-and-locales”

  • “point-free-topology” (or would that be “pointfree-topology”? or “pointless-topology”?)

I'm not too sure what the procedure is, both decisional and technical, to create a tag synonym, so I thought I'd better ask here, as well as what people think the best name would be.

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    $\begingroup$ Since you've mentioned tag synonyms, perhaps this could be tagged (tag-synonyms), too. (The tag-info for tag-synonyms contains a link to the FAQ post: What are tag synonyms and merged tags? How do they work? If you check the list of tag synonyms, you can see that most of the synonyms on MO were created by the moderators.) $\endgroup$
    – Martin Sleziak
    Apr 18, 2023 at 4:02
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    $\begingroup$ You can use [tag:locales] to create a direct link to a tag on the main site, e.g. locales. (For general knowledge, meta-tag should be used if you want to link to a tag on meta, e.g. tags.) $\endgroup$
    – Asaf Karagila Mod
    Apr 18, 2023 at 6:47
  • $\begingroup$ Just to clarify, in the proposed tag synonym, some newly created tag would be a master tag? Or is the suggestion to create a synonym where the existing tag (locales) would be a master tag - and some new tags would be added as synonyms? $\endgroup$
    – Martin Sleziak
    Apr 21, 2023 at 10:12
  • $\begingroup$ @MartinSleziak I'm a bit confused as to what the precise procedure is (and I was hoping someone would enlighten me in their answer… 😅). I think one would first create, say, frames-and-locales as a synonym for (the existing tag) locales, and later, if usage warrants it, moderators could merge the two tags into one (thereby retagging all questions with locales to the new tag). $\endgroup$
    – Gro-Tsen
    Apr 21, 2023 at 12:33
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    $\begingroup$ Re: I was hoping someone would enlighten me. Well that's why I posted (in the very first comment) a link to the FAQ post with information about the tag synonyms. I tried to mention a few things in the chatroom related to tagging - feel free to ping me there if some additional clarification is needed. When I asked which one is supposed to be the master tag, I was simply asking whether the tag synonym would be (locales) $\to$ (frames-and-locales) or the other way round. $\endgroup$
    – Martin Sleziak
    Apr 21, 2023 at 14:54
  • $\begingroup$ Maybe I'll mention just one more thing - since you do not have any answers in the tag (locales), even if this tag were to be the master tag, somebody else has to do the relevant actions in the user interface. (As you can see here: "Users with more than 2500 reputation and a total answer score of 5 or more on the tag, can suggest tag synonyms.") I guess chat would be a better place to discuss technicalities - and it is more important that in this discussion it is clarified what actually has to be done with this tag. $\endgroup$
    – Martin Sleziak
    Apr 22, 2023 at 3:42

3 Answers 3

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Since Martin Sleziak wrote an answer defending making the name pointless-topology the main tag (with locales and frames being, ultimately, synonyms of it), let me play the devil's advocate and defend making frames-and-locales the main tag (with the existing locales and also pointless-topology being synonyms of it). Actually I don't have strong opinions on the matter but having two opposing answers will make it possible to use their scores as a kind of straw poll between these options.

One reason why frames-and-locales might be a better choice is that it is slightly more general: the title of the present question notwithstanding, frames can be considered from the point of view of algebra (e.g., universal algebra) and/or order theory, not necessarily with a view toward generalized topology. In this case, the primary objects of study will be frames, locales are less likely to be of interest, and “pointless/pointfree topology” may not be an adequate description.

An example of this is J. Todd Wilson's thesis (“The Assembly Tower…”, 1994), which was referred to me in this answer, and which is about algebraic aspects of the category of frames: locales are barely mentioned past the introduction, and it's hard to argue that the thesis is about “topology”, pointfree or otherwise.

Another problem concerns the choice between the terms “pointless” and “pointfree” to qualify the topological study of locales: “pointless” is catchier and probably more memorable, but can be construed as derogatory and may be a misnomer because a pointless locale is one whose spatial part is empty, whereas “pointfree” topology describes the study of locales without qualification as to whether they have points or not.

The name frames-and-locales, on the other hand, clearly encompasses the algebraic study of frames as well as the topological study of locales, whether they have points or not.

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I suggest having two tags: and

We should have synonyms: [pointless-topology] for the first, and [frames-and-locales], [frames] and [locales] for the second.

We can put the suggestion in the tag wiki snippets to add the other tag of the pair. But it's not always true that someone thinking about frames is doing pointfree topology, and the name pointless/pointfree topology is going to be something people search for.

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  • $\begingroup$ Actually making the changes might be a bit subtle, but let's not worry about the technicalities of that. $\endgroup$
    – David Roberts Mod
    May 28, 2023 at 7:46
  • $\begingroup$ This is fine as far as I'm concerned, although I suspect a vast majority of the (already not very numerous) questions using one of these two tags would use the other. (But since most of these questions don't have a large number of tags anyway, it shouldn't be a problem.) $\endgroup$
    – Gro-Tsen
    May 28, 2023 at 8:55
  • $\begingroup$ I will add a link to a conversation in chat - just in case some stuff mentioned there might be useful for people interested in these tags. $\endgroup$
    – Martin Sleziak
    Jun 2, 2023 at 7:34
  • $\begingroup$ @Gro-Tsen I see that you have created a tag called (frames-and-locales). Is the intention to make (locales) and (frames) synonyms of this tag, as suggested in David Roberts' answer? $\endgroup$
    – Martin Sleziak
    Aug 25, 2023 at 4:40
  • $\begingroup$ @MartinSleziak Yes, “locales” at least. For “frames” it doesn't seem necessary because I don't believe anyone would think of using that word alone. $\endgroup$
    – Gro-Tsen
    Aug 25, 2023 at 8:21
  • $\begingroup$ @Gro-Tsen Would you perhaps be able to create a short tag-info for frames-and-locales? Considering the fact that a tag which has only one question and no tag-info is automatically removed after 6 months - for (frames-and-locales) this would happen in February. (Alternatively, one could add the tag to another question - if there are at least two questions, the tag is not removed by the script.) $\endgroup$
    – Martin Sleziak
    Dec 23, 2023 at 9:52
  • $\begingroup$ @MartinSleziak Thanks for pointing this out. I created a tag info and tagged a few of my own questions on the subject. $\endgroup$
    – Gro-Tsen
    Dec 23, 2023 at 10:20
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I would suggest to create a new tag - for example, this is the name used in the Wikipedia article. And then make the two tags and synonyms of this tag. (I.e., the tag would be the master tag.)

Naturally, since the tag would be entirely new, the synonym needs to be created by the moderators. (Only users with score $\ge5$ in the given tag can suggest synonyms - there won't be many such users in a newly created tag.)

Whether or not the tags will be merged should probably left for the decision of the moderators. (But waiting at least some time seems reasonable - to see whether somebody has objections to the synonym and in general whether the synonyms works reasonably.)

Among the tags mentioned above, the tag already exists, the two tags and would be new tags.

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  • $\begingroup$ Since nobody posted here any specific suggestion, I have posted at least one as an answer - so that other users can vote and comment to show whether or not they would consider this option reasonable or whether they prefer something else. $\endgroup$
    – Martin Sleziak
    Apr 22, 2023 at 5:40
  • $\begingroup$ One argument in favor of "pointless-topology" is that it might be easier for people new to the subject to remember, since it's a catchy name. $\endgroup$
    – Timothy Chow
    Apr 22, 2023 at 15:22
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    $\begingroup$ So, to (partially) play the devil's advocate, I've written another answer arguing that frames-and-locales is a better name than pointless-topology. $\endgroup$
    – Gro-Tsen
    Apr 24, 2023 at 16:23
  • $\begingroup$ I would love a pointless-analysis tag also. $\endgroup$
    – Dan Fox
    Apr 26, 2023 at 15:55
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    $\begingroup$ I would find it weird to characterise all questions on frames and locales as pointfree-topology. Locales also play roles in topos theory and logic that are not topological in nature. $\endgroup$
    – R. van Dobben de Bruyn
    Apr 27, 2023 at 15:21

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