Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Insertion of Continuous Set-Valued Mappings   An interesting insertion result about the existence of "intermediate"
set-valued mappings between pairs of given set-valued mappings was obtained by
Nepomnyashchii. His construction was for a paracompact domain, and he remarked
that his result is similar to Dowker's insertion theorem and may represent a
generalisation of this theorem. In the present paper, we characterise the
$\tau$-paracompact normal spaces by this insertion property and in the special
case of $\tau=\omega$, i.e. for countably paracompact normal spaces, we show
that it is indeed equivalent to Dowker's insertion theorem. Moreover, we obtain
a similar result for $\tau$-collectionwise normal spaces and show that for
normal spaces, i.e. for $\omega$-collectionwise normal spaces, our result is
equivalent to the Kat\v{e}tov-Tong insertion theorem. Several related results
are obtained as well.

16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat