Talk:Subspace of Subspace is Subspace

"Ambient space" is just a word to describe the result, much like "depend".


 * Still needs to be defined. As it stands, the title is too far different from the exposition for a novice to be able to make sense of it. --prime mover (talk) 16:59, 30 August 2017 (EDT)


 * Maybe. If we change the title, I'd certainly use "topology" and "depend". What about "Subspace Topology does not depend on Superset"? --barto (talk) 17:22, 30 August 2017 (EDT)


 * Moving a bit off-topic: Any attempt to define "ambient space" will probably result in a disambiguation with about 20 links to pages that are informal explanations rather than definitions. --barto (talk) 17:22, 30 August 2017 (EDT)


 * There exist the following options:


 * a) Rewrite the title so as not to use the term "ambient space".


 * b) Define the concept "ambient space". (It's a concept, it is not defined on, and if it is going to be used, it needs to be defined.) If it results in a "disambiguation with about 20 links to pages ..." that means either:
 * it cannot be defined accurately and precisely, and so it is not a mathematical term and so we don't use the word here
 * or:
 * it needs someone with better explanatory skill to define it.


 * What we do not do is leave technical terms undefined. --prime mover (talk) 18:25, 30 August 2017 (EDT)

As you can see this is not covered by Topological Subspace is Topological Space. --barto (talk) 16:52, 30 August 2017 (EDT)


 * No, not specifically, but there do exist a number of results that do the same sort of job. I believe they may cover it. --prime mover (talk) 16:59, 30 August 2017 (EDT)
 * I have been unable to find anything that already does this. If something does already exist, let me know and I’ll sort out the duplication. —Leigh.Samphier (talk) 07:43, 27 June 2019 (EDT)


 * Okay no worries. What's here is good. If we find duplication, we can place a mergeto template in there and it can then be covered as and when we get to it. --prime mover (talk) 11:13, 27 June 2019 (EDT)


 * A few weeks back I noticed that there were similar theorems that I could not find:
 * Subring of Subring is Subring
 * Subgroup of Subgroup is Subgroup
 * Restriction of Restriction of Operation is Restriction
 * Restriction of Restriction of Function is Restriction
 * Restriction of Restriction of Relation is Restriction
 * I wasn’t sure if I was being overly pedantic/pedestrian about this. I think these theorems are deemed so obvious that they are not stated. You rarely find them in a book. But it is common to move between a structure and it’s substructure in theorems and the substructure definition is designed to allow this. —Leigh.Samphier (talk) 17:25, 27 June 2019 (EDT)


 * If you can find them in a book then someone deems them worthy of stating. I can't see a need for such depth of detail myself.


 * As a subgroup, for example, is defined as being a subset of a group which is itself a group, then it means invoking "Subgroup is subset of group which is group, subgroup of subgroup is subset of subset of group which is group, the result follows from subset transitivity" -- and unless you are on shaky conceptual ground where you need to be very careful about whether or not you are "allowed" to use transitivity of subsets, it's probably a detail which can be taken for granted.


 * And the same applies to all such statements. But if you feel like posting them up, feel free. --prime mover (talk) 18:02, 27 June 2019 (EDT)