why say "$\mathbb{R}$-tree"?

Question

Definition. An $\mathbb{R}$-tree is a metric space $(X,d)$ such that

there is a unique geodesic segment (denoted $[x,y]$) joining each pair of points $x,y \in X$;

if $[x,y] \cap [y,z] = \{y\}$, then $[x,y] \cup [y,z] = [x,z]$.

why this space name is $\mathbb{R}$-tree ?

score 2 · Answer 1 · answered Sep 04 '14 at 05:18

2

Probably to differentiate it from a graph-theoretic tree (which is also a metric space, but a discrete one). An $\Bbb{R}$-tree is what you get by "filling in the gaps" between the vertices of a tree.

answered Sep 04 '14 at 05:18

Micah

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so What is $\mathbb{N}$-tree? – Sara Sep 04 '14 at 05:43
@Sara I never saw that term. Or $\mathbb Q$-tree, $\mathbb C$-tree, etc. – Nov 12 '14 at 02:11
There are trees on other groups as well. – Behnam Esmayli Aug 03 '22 at 12:23

why say "$\mathbb{R}$-tree"?

1 Answers1