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arXiv · 2406.17373

Covering $B_X$ by finitely many convex sets

Matias Raja
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Abstract

Given a finite covering by closed convex sets of $B_X$, 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 $1$ 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 $1/2$ and finite codimension under much more restrictive hypotheses.

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Matias Raja. 2024-06-25. Covering $B_X$ by finitely many convex sets. https://arxiv.org/abs/2406.17373

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