No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p

Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society.


Journal Article | Epub ahead of print | English

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Abstract
We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego, California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg theorem, the selection lemma and the weak 𝜀 ‐net theorem in Banach spaces of type 𝑝>1 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma.
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Date Published
2021-01-13
Journal Title
Bulletin of the London Mathematical Society
Acknowledgement
I wish to thank Imre Bárány for bringing the problem to my attention. I am grateful to Marton Naszódi and Igor Tsiutsiurupa for useful remarks and help with the text. The author acknowledges the financial support from the Ministry of Educational and Science of the Russian Federation in the framework of MegaGrant no 075‐15‐2019‐1926.
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Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. 2021. doi:10.1112/blms.12449
Ivanov, G. (2021). No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society. London Mathematical Society. https://doi.org/10.1112/blms.12449
Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society. London Mathematical Society, 2021. https://doi.org/10.1112/blms.12449.
G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p,” Bulletin of the London Mathematical Society. London Mathematical Society, 2021.
Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach spaces of type p. Bulletin of the London Mathematical Society.
Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach Spaces of Type P.” Bulletin of the London Mathematical Society, London Mathematical Society, 2021, doi:10.1112/blms.12449.
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arXiv 1912.08561

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