Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coarse structure of ultrametric spaces with applications   We show how to decompose all separable ultrametric spaces into a "Lego"
combinations of scaled versions of full simplices. To do this we introduce
metric resolutions of large scale metric spaces, which describe how a space can
be broken up into roughly independent pieces. We use these metric resolutions
to define the coarse disjoint union of large scale metric spaces, which
provides a way of attaching large scale metric spaces to each other in a
"coarsely independent way". We use these notions to construct universal spaces
in the categories of separable and proper metric spaces of asymptotic dimension
$0$, respectively. In doing so we generalize a similar result of Dranishnikov
and Zarichnyi as well as Nag\'orko and Bell. However, the new application is a
universal space for proper metric spaces of asymptotic dimension $0$, something
that eluded those authors. We finish with a description of some countable
groups that can serve as such universal spaces.

19
The categories of this paper are: eess
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int