Covering $B_X$ by finitely many convex sets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913719018061824 |
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| author | Raja, Matias |
| author_facet | Raja, Matias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17373 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Covering $B_X$ by finitely many convex sets Raja, Matias Functional Analysis 46B06, 46B20 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. |
| title | Covering $B_X$ by finitely many convex sets |
| topic | Functional Analysis 46B06, 46B20 |
| url | https://arxiv.org/abs/2406.17373 |