Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On universal minimal compact G-spaces   For every topological group G one can define the universal minimal compact
G-space X=M_G characterized by the following properties: (1) X has no proper
closed G-invariant subsets; (2) for every compact G-space Y there exists a
G-map X-->Y. If G is the group of all orientation-preserving homeomorphisms of
the circle S^1, then M_G can be identified with S^1 (V. Pestov). We show that
the circle cannot be replaced by the Hilbert cube or a compact manifold of
dimension >1. This answers a question of V. Pestov. Moreover, we prove that for
every topological group G the action of G on M_G is not 3-transitive.

33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat