Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cantor set of linear orders on N is the universal minimal
  S_\infty-system   Each topological group $G$ admits a unique universal minimal dynamical system
$(M(G),G)$. When $G$ is a non-compact locally compact group the phase space
$M(G)$ of this universal system is non-metrizable. There are however
topological groups for which $M(G)$ is the trivial one point system (extremely
amenable groups), as well as topological groups $G$ for which $M(G)$ is a
metrizable space and for which there is an explicit description of the
dynamical system $(M(G),G)$. One such group is the topological group $S_\infty$
of all permutations of the integers ${\mathbb Z}$, with the topology of
pointwise convergence. We show that $(M(S_\infty),S_\infty)$ is a symbolic
dynamical system (hence in particular $M(S_\infty)$ is a Cantor set), and give
a full description of all its symbolic factors. Among other facts we show that
$(M(G),G)$ (and hence also every minimal $S_\infty$) has the structure of a
two-to-one group extension of proximal system and that it is uniquely ergodic.

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The categories of this paper are: hep-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
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The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg