Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong Proximities on Smooth Manifolds and Vorono\" i Diagrams   This article introduces strongly near smooth manifolds. The main results are
(i) second countability of the strongly hit and far-miss topology on a family
$\mathcal{B}$ of subsets on the Lodato proximity space of regular open sets to
which singletons are added, (ii) manifold strong proximity, (iii) strong
proximity of charts in manifold atlases implies that the charts have nonempty
intersection. The application of these results is given in terms of the
nearness of atlases and charts of proximal manifolds and what are known as
Vorono\" i manifolds.

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The categories of this paper are: stat
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The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
1
The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th