Covering $B_X$ by finitely many convex sets
Functional Analysis
2025-03-06 v2
Abstract
Given a finite covering by closed convex sets of , the unit ball of an infinite-dimensional Banach space, we investigate whether there is a set of the covering that contains balls of radius close to and (a) arbitrarily high finite dimension or (b) infinite dimension. In case (a) the answer is affirmative, but for the case (b) we just get radius close to and finite codimension under much more restrictive hypotheses.
Cite
@article{arxiv.2406.17373,
title = {Covering $B_X$ by finitely many convex sets},
author = {Matias Raja},
journal= {arXiv preprint arXiv:2406.17373},
year = {2025}
}