Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On universal continuous actions on the Cantor set   Using the notion of proper Cantor colorings we prove the following theorem.
For any countably infinite group $\Gamma$, there exists a free continuous
action $\zeta: \Gamma \curvearrowright C$ on the Cantor set, which is universal
in the following sense: for any free Borel action $\alpha: \Gamma
\curvearrowright X$ on the standard Borel space, there exists an injective
Borel map $\Theta_\alpha: X\to C$ such that $\Theta_\alpha\circ \alpha=\zeta
\circ \Theta_\alpha$. We extend our theorem for (nonfree) Borel
$(\Gamma,Z)$-actions, where $Z$ is a uniformly recurrent subgroup.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org