Reference for ultrametric spaces I have a research project involving ultrametric spaces, and there are some facts that I use but have a hard time finding explicitely in the literature, although I know that some of them are folklore (for example, an ultrametric space can be described as the set of leaves of a tree, endowed with the induced metric).
I would like to know whether there is a book or comprehensive survey paper on the geometry and structure of ultrametric spaces.
An important point: I am interested in purely metric spaces, without algebraic structure (I did find books on analysis in non-Archimedean fields, which are too focused on this case). I can restrict to compact spaces, but not to finite ones.
 A: Maybe the following paper and references in there:


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*MR2026825 (2005j:54018)
Lemin, Alex J.(RS-MSUCE)
The category of ultrametric spaces is isomorphic to the category of complete, atomic, tree-like, and real graduated lattices LAT∗. (English summary) 
Algebra Universalis 50 (2003), no. 1, 35–49. 

A: What about 

MR2093482 (2005m:57001)
  Hughes, Bruce.
  Trees and ultrametric spaces: a categorical equivalence. (English summary).
  Adv. Math. 189 (2004), no. 1, 148–191.

It's not a survey, but it deals with the correspondence between ultrametric spaces and the ends of a tree.
From the review on mathscinet: 
`The author studies the correspondence between infinite trees and ultrametric spaces arising from the end space of the tree. The main theorem is the existence of an equivalence defined from the category of geodesically complete, rooted $\mathbb{R}$-trees and equivalence classes of isometries at infinity, to the category of complete ultrametric spaces of finite diameter and local similarity equivalences.' 
