Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hausdorff Mapping Is Nonexpanding   In the present paper we investigate the properties of the Hausdorff mapping
$\mathcal{H}$, which takes each compact metric space to the space of its
nonempty closed subspaces. It is shown that this mapping is nonexpanding
(Lipschitz mapping with constant $1$). This paper gives several examples of
classes of metric spaces, distances between which are preserved by the mapping
$\mathcal{H}$. We also calculate distance between any connected metric space
and any simplex with greater diameter than the former one. At the end of the
paper we discuss some properties of the Hausdorff mapping which may help to
prove that it is isometric

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The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs