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There exists a tag named , the tag-info is empty at the moment.

The notion of quotient space appears in various areas. It can be defined for topological spaces, vector spaces, normed spaces and probably also in some other context which I might be unaware of.

I think that it could be useful to clarify in the tag-excerpt and tag-wiki for what kind of questions the tag should be used for.

Is it suitable for all areas which I have mentioned above? Are there some other which I did not mention and where the tag could be suitable? Or should we restrict usage of this tag only for one of the above-mentioned meanings?

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  • $\begingroup$ Quotient spaces are sets of equivalences classes, so another possible use is in the context of relations. $\endgroup$
    – Git Gud
    Dec 3, 2014 at 14:56
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    $\begingroup$ @GitGud Wouldn't the tags (equivalence-relations) and perhaps (partitions) more suitable for such questions? $\endgroup$
    – Martin Sleziak
    Dec 3, 2014 at 14:57
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    $\begingroup$ Since the tag can be used in conjunction with (group-theory), (vector-spaces), etc, I think there's something to lose in restricting the use to only one area of mathematics. $\endgroup$
    – Git Gud
    Dec 3, 2014 at 14:58
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    $\begingroup$ You're right. In my native language sets of equivalence classes are called 'quotient sets', so I guess the name is more suggestive in my language than in english. $\endgroup$
    – Git Gud
    Dec 3, 2014 at 15:00

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I would be in favour of including in the tag info some direction asking the user to (not in the precise words below, but along the lines of)

... also include a tag specifying subject matter, such as (topology), (vector-spaces), (normed-spaces), etc.

We do this already in some other tags ( and come to mind), and this may be another case of the same.

I think of this type of treatment whenever the tag deals with a large theme/concept that appears frequently over many branches of mathematics; this is distinct from the case of disjoint concepts in different fields that happen to share the same name.

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  • $\begingroup$ The question has been around for some time and this is the most upvoted answer. So I went ahead and edited the tag-excerpt and the tag-wiki. $\endgroup$
    – Martin Sleziak
    Apr 17, 2015 at 7:24
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I would be happy restricting this tag to topological contexts. Although the quotient construction is fairly pervasive in mathematics, algebraic contexts including vector spaces make this such a routine tool that I suspect including those in the tag would dilute its value for delineating (searching) among point set and simplicial topology questions.

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If the tag is kept, I think it would be preferable to restrict it to quotients of vector spaces (and closely related structures). Meanwhile, a or tag could be introduced to handle questions about, well, quotient topologies. (Other quotient structures could also be given their own tag.)

(I am not entirely convinced that the tag should be kept, but this is one way towards disambiguating the tag, instead of keeping it as a quasi-meta-tag.)

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