---
_id: '9037'
abstract:
- lang: eng
text: "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 \U0001D700 ‐net theorem in Banach spaces
of type \U0001D45D>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."
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.\r\nThe 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."
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Grigory
full_name: Ivanov, Grigory
id: 87744F66-5C6F-11EA-AFE0-D16B3DDC885E
last_name: Ivanov
citation:
ama: Ivanov G. No-dimension Tverberg’s theorem and its corollaries in Banach spaces
of type p. Bulletin of the London Mathematical Society. 2021;53(2):631-641.
doi:10.1112/blms.12449
apa: 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
chicago: 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.
ieee: G. Ivanov, “No-dimension Tverberg’s theorem and its corollaries in Banach
spaces of type p,” Bulletin of the London Mathematical Society, vol. 53,
no. 2. London Mathematical Society, pp. 631–641, 2021.
ista: Ivanov G. 2021. No-dimension Tverberg’s theorem and its corollaries in Banach
spaces of type p. Bulletin of the London Mathematical Society. 53(2), 631–641.
mla: Ivanov, Grigory. “No-Dimension Tverberg’s Theorem and Its Corollaries in Banach
Spaces of Type P.” Bulletin of the London Mathematical Society, vol. 53,
no. 2, London Mathematical Society, 2021, pp. 631–41, doi:10.1112/blms.12449.
short: G. Ivanov, Bulletin of the London Mathematical Society 53 (2021) 631–641.
date_created: 2021-01-24T23:01:08Z
date_published: 2021-04-01T00:00:00Z
date_updated: 2023-08-07T13:35:20Z
day: '01'
ddc:
- '510'
department:
- _id: UlWa
doi: 10.1112/blms.12449
external_id:
arxiv:
- '1912.08561'
isi:
- '000607265100001'
file:
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checksum: e6ceaa6470d835eb4c211cbdd38fdfd1
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creator: kschuh
date_created: 2021-08-06T09:59:45Z
date_updated: 2021-08-06T09:59:45Z
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file_name: 2021_BLMS_Ivanov.pdf
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intvolume: ' 53'
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issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc-nd/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 631-641
publication: Bulletin of the London Mathematical Society
publication_identifier:
eissn:
- '14692120'
issn:
- '00246093'
publication_status: published
publisher: London Mathematical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: No-dimension Tverberg's theorem and its corollaries in Banach spaces of type
p
tmp:
image: /images/cc_by_nc_nd.png
legal_code_url: https://creativecommons.org/licenses/by-nc-nd/4.0/legalcode
name: Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
(CC BY-NC-ND 4.0)
short: CC BY-NC-ND (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 53
year: '2021'
...