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math.FA2026
On Banach Spaces with the Helly Approximation Property
Grigory Ivanov
Qualitatively, a no-dimensional Helly-type theorem says that if every small subfamily of convex sets has a common point in a bounded region, then suitable neighborhoods of all the…
math.FA2026
No-dimensional results of combinatorial convexity. Dimension strikes back
Grigory Ivanov
We discuss no-dimensional (approximate) versions of Carathéodory's and Helly's theorems. Our goal is to draw attention to open problems and potential applications related to these…
math.FA2024
No-dimensional Helly's theorem in uniformly convex Banach spaces
G. Ivanov
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 sp…