# Should we blacklist [homeomorphism]?

In the past few days, I've been repeatedly removing the tag. I don't see why this tag is useful, it adds nothing to the question, it adds nothing to its classification.

Perhaps it is time to make sure that this tag stays dead?

Or maybe I'm wrong, and the tag is indeed useful?

• Keep in mind that a tag's purpose is to help with searching, not for "adding to" or clarifying the Question. The searching here is not only what we do "manually" but the automated searching done to populate the Related links in the sidebar and some other system features. – hardmath Nov 14 '16 at 11:38
• It seems this tag is already gone...??? – GEdgar Nov 14 '16 at 13:10
• @hardmath: True, but the word "homeomorphism" is fairly easy to search for; so I'm not sure that the tag is useful for searching purposes. – Asaf Karagila Nov 14 '16 at 14:43
• @GEdgar as explained in the post Asaf repeatedly 'killed' the tag. Now he wants to make sure that "this tag stays dead" via blacklisting it. That is, the point of the post is not to get the tag delete but to get it added to a list of 'forbidden tag names,' which cannot be used (re)create a tag in the future. – quid Nov 14 '16 at 17:12
• What would you think about making [homeomorphism] a synonym for [topology] ? Personally I would prefer this approach to blacklisting, if something needs to be done. – hardmath Nov 14 '16 at 20:14
• @hardmath: I am definitely amenable to this solution. I don't think it's a useful tag, but if others disagree then it's not a bad halfway. The problem, though, is that it will cause a "duplicate tag" (as most of these questions already carry the general topology tag), which may confuse users. – Asaf Karagila Nov 14 '16 at 20:18
• here is a recently posted question that deserves the tag homeomorphism (though it does not have it at present) : math.stackexchange.com/q/2015499 – Mirko Nov 15 '16 at 19:45
• @Mirko: I'm not entirely sure. I do agree it might be more deserving than other questions, but I don't know if a handful of deserving questions is a good excuse for a tag. – Asaf Karagila Nov 15 '16 at 19:51
• I think 'homeomorphism' could be useful as a tag in some contexts, even though I understand the risks of people using it incorrectly. However, is this really such a problem that we should ban a tag based on the difficulty of using it appropriately? Instead of answering how it does not help the community, could we answer to what extent it harms it? – Christopher.L Nov 25 '16 at 18:23
• @Christopher: Yes. If the risk is high enough, it's not worth it. – Asaf Karagila Nov 25 '16 at 20:43

I think the homeomorphism tag is quite useful in the sense that it helps answerers and viewers to know that a particular question must be answered by constructing homeomorphisms explicitly or the question is about algebraic topology. Without the tag, confusion may arise as to whether the question is an analytic or topological one.

• Neither of the recent questions was in algebraic topology, though. And I don't recall older questions being about algebraic topology either. This tag is too easy to abuse, namely people asking a question where a homeomorphism appears can---and will---add this tag just because they don't know what tags should be there. I don't dispute that it can have useful aspects, but it is too easy to abuse, as done until now, which means it's not up to a great start anyway. – Asaf Karagila Nov 14 '16 at 3:42
• This answer appears very confused, and seems to betray an unfamiliarity with the topic. Can you, for instance, point to even a single question where the absence of this tag makes it unclear that a question is either topological or analytic? There are a wide range of questions in topology which neither require "constructing homeomorphisms explicitly" nor are about algebraic topology (or analysis). – user642796 Nov 16 '16 at 12:04
• @arjafi Consider the problem of proving a certain set open/closed in $\mathbb{R} \times S^1$. Instead of going from basics, knowing that it is homeomorphic to $\mathbb{R}^2-0$ can sometimes save us the labour, isnt it? – vidyarthi Nov 17 '16 at 7:53

Yeah, it might be time to request a blacklist.

First of all, I really don't see what value is added by the tag. At one point there seems to have been a tag-wiki for the tag which read

Homeomorphisms are continuous functions with continuous inverses. They are important in topology as they capture they preserve all topological properties.

This said absolutely nothing about the usage of the tag, only described the concept. An SEDE query gives a list of currently undeleted questions which at one point had this tag, and it is entirely underwhelming.

A fair number of these have nothing to do with homeomorphisms, and another large contingent deal with whether topological spaces are homeomorphic, which even in the positive can sometimes be answered without "constructing homeomorphisms explicitly" (to borrow a phrase from vidyarthi's answer).

Setting aside the issue of its historical usage, I cannot really think of what it is attempting to isolate. Is it for questions about properties of homeomorphisms? (A fairly bland topic, IMHO.) Is it for questions about "explicitly" constructing homeomorphisms? (But in the case of questions concerning non-homeomorphic spaces what then?) Is it for questions about the existence of homeomorphisms? (But at some level topology is wholly concerned with this question, so maybe it's just a synonym.)

So, yeah, I cannot see any redeeming value in the tag.

Taking a closer look at the data from the SEDE query we see numerous points where the tag has seemingly resurfaced: mid-2013, Dec 2014, Dec 2015, Feb 2016, July 2016, and now in Nov 2016. This seems to indicate that this poor tag regularly reappears, and of late has been reappearing pretty frequently.

So let's unleash Trogdor the Burninator!

• Go Trogdor!!! StrongBad is proud. – Asaf Karagila Nov 14 '16 at 20:24
• @Asaf. Maybe. But I'll probably have to go to the Teachers' Lounge to be sure. – user642796 Nov 14 '16 at 20:27
• Touché. But I think it's not the same one... – Asaf Karagila Nov 14 '16 at 20:30
• Thanks, Trogdor just reminded me that my laptop volume is at its maximum... – copper.hat Nov 15 '16 at 5:04
• I disagree with the interpretation of this list. I believe that in 12 out of the 17 questions listed, the word homeomorphism seems appropriate. I am against deleting a tag based on personal opinions (e.g statement of "bland topic, IMHO"). @Asaf might have a point (since he is doing the work of removing the tag, and I am not), but nevertheless my guts feeling is that this tag is worth existing, and has its place, used appropriately. I think this is not the only tag abused by people that may not know which tag to use, and it looks like just picking on this particular one. Have mercy on it :) – Mirko Nov 15 '16 at 17:01
• @Mirko: It pains me to see the logic and proof theory tags misused as often as they do, as is the set theory tags (oh, there are sets involved, must be set theory!). But those have importance, these are fields in mathematics, and actual topics. Homeomorphism is a type of function, the tag adds very little search value, and it's unclear what should go in there so it's open to misuse. Here I'm "picking on it" because it is so small, and we can still "fix" the situation by removing it, and we have the privilege of not having it without losing as much (compared to not having set theory tags). – Asaf Karagila Nov 15 '16 at 19:49
• @Mirko Generously, I think that 6 of those 17 questions are really about homeomorphisms (noting that questions about whether spaces are homeomorphic are rather tangentially about homeomorphisms; or are about homeomorphisms as much they are about general functions, or relations, or sets). There has never been any guidance for the use of this tag, and no-one here has suggested any. Those who, like you, find value in this tag should figure this out, at a bare minimum. Otherwise you're offering less than a personal opinion as to why it shouldn't be blacklisted. – user642796 Nov 16 '16 at 12:11
• @arjafi Well, 6 is a positive number, even if this is all you think is really about homeomorphisms. What harm does the existence of this tag pose to the community? How would people that might need it be able to express themselves? There is an influential 1966 general topology paper by Arhangelski, called Mappings and Spaces, and there is AMS subj class 54C Maps and general types of spaces defined by maps (continuous, open, closed maps, etc). Homeomorphism in an important type of map, the tag may provide "fine tuning" after a more basic tag, e.g. "general topology" has been already selected. – Mirko Nov 16 '16 at 14:30
• @Mirko: But 6 is not a sufficient number to justify a tag. Even in the bible, for 50 righteous people God would have spared Sodom and Gomorrah; but for one, God told Abraham to get that person out. I don't know what's "enough" for a tag, but 6 is not one that I think justifies that. – Asaf Karagila Nov 16 '16 at 15:00
• @Asaf I put my 2 cents in, and I would never admit it is right to delete a tag as it is in my nature to not throw out anything. But I admit you are in a better position to see and judge what you are talking about (and to take action, as you deem necessary). Perhaps my talk about mappings (open, closed, etc) might give an idea for a new tag (which might include homeomorphisms, as in 54C), but that is another matter. One thing that I am unclear about is: Why is the mere existence of a (perhaps an unnecessary) tag supposed to be nuisance? (Perhaps "clutter" is the answer, I don't know.) Thank you – Mirko Nov 16 '16 at 17:13
• So... now what? We're at an impasse. Only four people have voiced their opinion on your agreement that we should blacklist; 15 people voiced their opinion on the validity of the request (or their support of that request, it's unclear how to read the votes on the question, since those people should have been voting on this answer as well); and 11 people voiced an opinion on vidyarthi's answer, which seems to have an important discussion in the comment going nowhere. So... what do we do? – Asaf Karagila Nov 20 '16 at 7:25
• @Asaf I guess the blacklist is a non-starter. At least there doesn't appear to be a community consensus about it. But until someone can actually come up with usage guidance for such a tag, I think it's fair to remove it when seen. I haven't noticed it come back in the last week or so, so maybe we'll be okay until the end of the year. – user642796 Nov 20 '16 at 8:07