Talk:Real tree

Disambiguation

may want disambiguation from real tree camouflage

First section is misleading

In the first sentence on this page, it is written that a real tree is a uniquely geodesic metric space. This is of course not true, since the condition that "any geodesic triangle is a tripod" is missing. Instead of lengthily explaining what "arc" and "geodesic" means (this is explained in the respective articles and does not need to be repeated here), I would correct and clarify what real trees are. The second section ... a geodesic metric space M is a real tree if and only if M is a δ-hyperbolic space with δ=0. is true and much better. — Preceding unsigned comment added by 129.132.147.26 (talk) 10:24, 23 September 2013 (UTC)

Too technical

Topology is often studied at the end of undergraduate math training. Therefore, in the spirit of writing "one level down" (see: WP:UPFRONT), this article should ideally include an intro that is much more comprehensible to someone with some relatively advanced high school math training (say, through a year of calculus). I don't understand the subject well enough to write such an intro, unfortunately... Aroundthewayboy (talk) 04:48, 26 July 2015 (UTC)

I revised the page to make the mathematical content more interesting and (hopefully) better organised, but the new intro I wrote may still fall short of what you want. On the other hand this is not a topic that arises in elementary mathematics (as made obvious by the examples) so I feel that giving the context by linking to the geometric group theory and brownian tree pages might give the mathematically unsophisticated reader an idea of what this thing is for. Jean Raimbault (talk) 16:05, 10 April 2016 (UTC) Jean Raimbault

Two independant remarks

In the section "Definitions and Exemples", "Formal Definition", the redirection to "geodesic" is pointless, it needs a redirection to "geodesic metric space" but unfortunately such a page doesn't exist (and should be created !).

Also, in "Simple Examples" it is said in the first point "a real tree is simplicial if and only if the set of singular points is discrete in X" and in the second point it is given an exemple of a real tree with a discrete set of singular points which is not simplicial, which is quite a contradiction.

If nobody disagrees or makes the changes, I will correct the redirection and the example.

Tilwen (talk) 11:23, 5 September 2017 (UTC)

Both of these sound like clear improvements to me — please go ahead and do them. —David Eppstein (talk) 16:17, 5 September 2017 (UTC)

For the second remark the correction should be to add the condition that the singular set be closed in addition to discrete (this is something I mistakenly left out when I reorganised a previous version of this article, see the section "simplicial R-trees" in this older version: https://en.wikipedia.org/w/index.php?title=Real_tree&oldid=670014169) jraimbau (talk) 12:23, 6 September 2017 (UTC)

Surely an error

In Characterizations, item 4) seems to be a a class of examples, but not an equivalent condition. The trees described are always compact, so they can't be fully general. 2A02:1210:2642:4A00:4DF:8368:7F16:87DF (talk) 23:46, 18 June 2023 (UTC)