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The current use of tag named "norm" is actually meant normed vector spaces. But it is not different from the tag "normed-spaces" Unfortunately, I cannot propose this as a tag-synonym due lack of reputation on this particular tag :).

On the other hand, this use can be misleading as we can equip many algebraic structures with a compatible metric to define their normed counterparts. In fact, normed groups, normed rings, normed fields, normed algebras (and many more) are useful and well established concepts.

So, here I have two proposals:

  1. Merge them to make a tag "normed-vector-spaces".
    I am well aware that people use normed space as a shorthand for normed vector spaces, but I don't think writing the full name would do any harm :)

  2. Recycle the tag name "norm" in the inclusive sense to capture all the above mentioned notions.
    Some of you may find this is unnecessary as we currently have no questions in this sense. At first, I was actually formulating a question about a topological semigroup whose topology is metrizable before I found this possible loophole. It will only be a matter of time until we receive questions about general norms.

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    $\begingroup$ please see math.meta.stackexchange.com/questions/32974/tag-management-2021 $\endgroup$
    – Albus Dumbledore
    Apr 4, 2021 at 2:50
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    $\begingroup$ You say that you cannot propose a tag-synonym. The proposal for a tag-synonym norm $\to$ normed-spaces already exists. As I said before, I think that something which influences so many posts should definitely be discussed on meta first. (However, you seem to be proposing a new tag, and you suggest merging - which is different from a synonym. One should be a bit careful with merging, since it is not a reversible process - unlike synonym.) $\endgroup$
    – Martin Sleziak
    Apr 4, 2021 at 6:09
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    $\begingroup$ @AlbusDumbledore Personally, I think this deserves a separated question. One of the tags has about 5k questions, to other one about 4k questions - I think that anything which affects that many posts should be discussed thoroughly. $\endgroup$
    – Martin Sleziak
    Apr 4, 2021 at 6:41
  • $\begingroup$ @MartinSleziak the tag synonym is 1 vote away from being automatically accepted by the system. This may take forever or it may take 20 minutes; would it be preferred if I retracted my vote to make this less likely? (Casted it a long time ago) $\endgroup$
    – Calvin Khor
    Apr 4, 2021 at 23:40
  • $\begingroup$ I’m not sure if this is related, but there is also the [absolute-value] tag which holds the more algebraic variant (if $d$ is the discrete metric, then $d(x,0)$ is an ‘absolute value’ but not a norm which I learned from eg this discussion ) does this tag suffice for you? I have no idea if the norms on algebraic structures are of this type. $\endgroup$
    – Calvin Khor
    Apr 4, 2021 at 23:50
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    $\begingroup$ The term norm is even more overloaded in math than your list of examples implies. For example not all norms are real valued. Therefore I am not sure how useful it is as a tag. True, we can use the tag wikis to guide people. IMO the tag wikis should then explain what is the appropriate tag when the intended use of the asker is not within the scope agreed upon by the tag wiki creators. $\endgroup$
    – Jyrki Lahtonen
    Apr 6, 2021 at 4:29
  • $\begingroup$ My knee-jerk reaction is that if you want a tag that covers the uses on your list and nothing else, then normed-spaces is a better choice than norm. $\endgroup$
    – Jyrki Lahtonen
    Apr 6, 2021 at 4:32
  • $\begingroup$ For that reason I downvoted this proposal. Please don't take that personally. I totally appreciate your attempt to improve the tagging system. It is just that overloaded terms as tags lead to confusion. I think we can find several instances of that happening in the past. $\endgroup$
    – Jyrki Lahtonen
    Apr 6, 2021 at 4:39

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