Year: 2025
Type: article
Abstract: We study the “no-dimensional” analogue of Helly’s theorem in Banach spaces. Specifically, we obtain the following no-dimensional Helly-type results for uniformly convex Banach spaces: Helly’s theorem, fractional Helly’s theorem, colorful Helly’s theorem, and colorful fractional Helly’s theorem. The combinatorial part of the proofs for these Helly-type results is identical to the Euclidean case as presented in [2]. The primary difference lies in the use of a certain geometric inequality in place of the Pythagorean theorem. This inequality can be explicitly expressed in terms of the modulus of convexity of a Banach space.
Author: Grigory Ivanov
Institution: Pontifícia Universidade Católica do Rio de Janeiro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4409108815