Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pro-Lie groups which are infinite-dimensional Lie groups   A pro-Lie group is a projective limit of a family of finite-dimensional Lie
groups. In this note we show that a pro-Lie group $G$ is a Lie group in the
sense that its topology is compatible with a smooth manifold structure for
which the group operations are smooth if and only if $G$ is locally
contractible. We also characterize the corresponding pro-Lie algebras in
various ways. Furthermore, we characterize those pro-Lie groups which are
locally exponential, that is, they are Lie groups with a smooth exponential
function which maps a zero neighborhood in the Lie algebra diffeomorphically
onto an open identity neighborhood of the group.

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The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
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The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
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The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas