Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Completely Metrisable Groups Acting on Trees   We consider actions of completely metrisable groups on simplicial trees in
the context of the Bass--Serre theory. Our main result characterises continuity
of the amplitude function corresponding to a given action. Under fairly mild
conditions on a completely metrisable group $G$, namely, that the set of
elements generating a non-discrete or finite subgroup is somewhere dense, we
show that in any decomposition as a free product with amalgamation,
$G=A\ast_CB$, the amalgamated groups $A$, $B$ and $C$ are open in $G$.

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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: physics