Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differentiable spaces that are subcartesian   We show that the differential structure of the orbit space of a proper action
of a Lie group on a smooth manifold is continuously reflexive. This implies
that the orbit space is a differentiable space in the sense of Smith, which
ensures that the orbit space has an exterior algebra of differenial forms,
which statisfies Smith's version of de Rham's theorem. Because the orbit space
is a locally closed subcartesian space, it has vector fields and their flows.

18
The categories of this paper are: econ
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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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: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: patt-sol