Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on symmetric separation in Banach spaces   We present some new results on the symmetric Kottman's constant $K^s(X)$ of a
Banach space $X$ and its relationship with the Kottman constant. We show that
$K^s(X)>1$, for every infinite-dimensional Banach space, thereby solving a
problem by J.M.F. Castillo and P.L. Papini. We also investigate such constant
in the class of Banach spaces admitting $c_0$ spreading models, answering in
particular one question from our previous joint paper with P. H\'ajek and T.
Kania.

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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con