Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Helly-type theorems for the diameter   We study versions of Helly's theorem that guarantee that the intersection of
a family of convex sets in $R^d$ has a large diameter. This includes colourful,
fractional and $(p,q)$ versions of Helly's theorem. In particular, the
fractional and $(p,q)$ versions work with conditions where the corresponding
Helly theorem does not. We also include variants of Tverberg's theorem,
B\'ar\'any's point selection theorem and the existence of weak epsilon-nets for
convex sets with diameter estimates.

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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc