Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal equivariant compactifications   Let $G$ be a locally compact group. Then for every $G$-space $X$ the maximal
$G$-proximity $\beta_G$ can be characterized by the maximal topological
proximity $\beta$ as follows: $$ A \ \overline{\beta_G} \ B \Leftrightarrow
\exists V \in N_e \ \ \ VA \ \overline{\beta} \ VB. $$ Here, $\beta_G \colon X
\to \beta_G X$ is the maximal $G$-compactification of $X$ (which is an
embedding for locally compact $G$), $V$ is a neighborhood of $e$ and $A \
\overline{\beta_G} \ B$ means that the closures of $A$ and $B$ do not meet in
$\beta_G X$. Note that the local compactness of $G$ is essential. This theorem
comes as a corollary of a general result about maximal $\mathcal{U}$-uniform
$G$-compactifications for a useful wide class of uniform structures
$\mathcal{U}$ on $G$-spaces for not necessarily locally compact groups $G$. It
helps, in particular, to derive the following result. Let $(\mathbb{U}_1,d)$ be
the Urysohn sphere and $G=Iso(\mathbb{U}_1,d)$ is its isometry group with the
pointwise topology. Then for every pair of subsets $A,B$ in $\mathbb{U}_1$, we
have $$ A \ \overline{\beta_G} \ B \Leftrightarrow \exists V \in N_e \ \ \
d(VA,VB) > 0. $$ More generally, the same is true for any
$\aleph_0$-categorical metric $G$-structure $(M,d)$, where $G:=Aut(M)$ is its
automorphism group.

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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an