Definition talk:Support

Can we make this a disambiguation page? There are so many notions of support; those for permutations and direct products aren't even there yet. --barto (talk) 15:24, 16 December 2016 (EST)

Also, it does not make much sense to categorize this as Definitions/Analysis if we include notions of support that are non-analytical. --barto (talk) 15:57, 16 December 2016 (EST)

If we have instances of a definition of support that are analytical then it does make sense to include an "analysis" category.

All the definitions are consistent with each other, and "mean the same sort of thing", which justifies the transclusion approach. --prime mover (talk) 03:08, 17 December 2016 (EST)

Okay. (I'm in the process of getting acquainted with some of the more subtle conventions.) That makes me wondering if the general page should have the categories of all of its entries. --barto (talk) 03:31, 17 December 2016 (EST)

When it started, it did. :-)

I concede, having looked at it a little longer (be gentle with me, it's the morning after the night before) there may be a case for separating out the notions. It would help if you were to cite your sources for all these definitions that are coming out, so we have the chance of reading around the subject and see where this is all going. --prime mover (talk) 04:53, 17 December 2016 (EST)

I will look for some references. Where this is going: support of permutations should eventually serve to characterize normal subgroups of infinite symmetric groups; support in the context of direct products will be used in proofs that Definition:External Direct Sum is closed. --barto (talk) 05:35, 17 December 2016 (EST)

For all (or almost all?) of the notions of support there is a result that says something like Support of Product is Contained in Union of Supports; though the proof of that depend slightly on the notion. Is it sensible to have a proof page with transclusions? --barto (talk) 03:41, 17 December 2016 (EST)

I don't see why not. --prime mover (talk) 04:50, 17 December 2016 (EST)

Okay. What do you think is better: Support of Product is Contained in Union of Supports or just Support of Product? I don't much like long page titles; but they have to be transparent... --barto (talk) 05:20, 17 December 2016 (EST)

The longer one --prime mover (talk) 06:00, 17 December 2016 (EST)

To provide some rationale for PM's vote: We have had a lot of trouble with shorter names in the past (e.g. conflicts for different kinds of, in this case, supports; or issues with conditions on the result). So it's better to take the ugly, longer name. In the end it's just a web page :). — Lord_Farin (talk) 15:57, 18 December 2016 (EST)

I'd like to start organizing this page, using a disambiguation page (as mentioned somewhere above). Concretely, to make Definition:Support a disambiguation for:

• Definition:Support of Mapping
• Definition:Support of Distribution
• Definition:Support of Permutation
• Definition:Support (Direct Product)

That is, I request to move the corresponding subpages of Definition:Support.

The reason is that, while these definitions have philosophically common roots, they are otherwise unrelated.

As regards the definition of support for continuous functions (using closure) and the one for characteristic functions, I suggest to for example transclude them in Definition:Support of Mapping. It may perhaps be arguably more appropriate to put them separately in something like Definition:Support of Continuous Mapping, but I suggest not to focus on this sub-issue for now. --barto (talk) 10:35, 31 May 2017 (EDT)

Ultimately, though, each of those definitions of "support" mean exactly the same thing: the set of things that don't map to the identity element.

The point of a disambiguation page is to separate out completely different things which happen to have the same word to define them. An example (to pull one at random) is "Baire space". This is not one of those cases, because in all cases the "support" is the same thing. Hence the decision not to use a disambiguation page, but a general-definition-with-transclusions page, in exactly the same manner as for, for example, the section on homomorphisms and so on. This was the original design philosophy behind the usage of disambiguation pages in $\mathsf{Pr} \infty \mathsf{fWiki}$.

So where the definitions are all instances of the same thing, which is what this is, the transclusion techique wins out. --prime mover (talk) 13:17, 31 May 2017 (EDT)

I concede that this is not consistent in the current use of disambiguations (an example being "altitude"), and sooner or later this will need to be addressed to make it consistent. --prime mover (talk) 13:17, 31 May 2017 (EDT)

Okay. It's getting a bit messy though. I thought that, in the same spirit as the fact that we have Definition:Order of Group Element, Definition:Multiplicative Order of Integer, Definition:Root of Unity/Order some of the notions of support qualify to have their own page. But never mind. --barto (talk) 05:51, 4 June 2017 (EDT)