Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equilateral dimension of some classes of normed spaces   An equilateral dimension of a normed space is a maximal number of pairwise
equidistant points of this space. The aim of this paper is to study the
equilateral dimension of certain classes of finite dimensional normed spaces.
The well-known conjecture states that the equilateral dimension of any
$n$-dimensional normed space is not less than $n+1$. By using an elementary
continuity argument, we establish it in the following classes of spaces:
permutation-invariant spaces, Orlicz-Musielak spaces and in one codimensional
subspaces of $\ell^n_{\infty}$. For smooth and symmetric spaces,
Orlicz-Musielak spaces satisfying an additional condition and every
$(n-1)$-dimensional subspace of $\ell^{n}_{\infty}$ we also provide some weaker
bounds on the equilateral dimension for every space which is sufficiently close
to one of these. This generalizes the result of Swanepoel and Villa concerning
the $\ell_p^n$ spaces.

9
The categories of this paper are: nlin
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
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The categories of this paper are: quant-ph