How many sprays cover the space?
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910047629475840 |
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| author | Andretta, Alessandro Izmestiev, Ivan |
| author_facet | Andretta, Alessandro Izmestiev, Ivan |
| contents | For all $d \geq 3$ we show that the cardinality of $ \mathbb{R} $ is at most $\aleph_n $ if and only if $ \mathbb{R}^d $ can be covered with $ ( n + 1 ) ( d - 1 ) + 1 $ sprays whose centers are in general position in a hyperplane. This extends previous results by Schmerl when $ d = 2 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How many sprays cover the space? Andretta, Alessandro Izmestiev, Ivan Logic Metric Geometry 03E50, 51N20 For all $d \geq 3$ we show that the cardinality of $ \mathbb{R} $ is at most $\aleph_n $ if and only if $ \mathbb{R}^d $ can be covered with $ ( n + 1 ) ( d - 1 ) + 1 $ sprays whose centers are in general position in a hyperplane. This extends previous results by Schmerl when $ d = 2 $. |
| title | How many sprays cover the space? |
| topic | Logic Metric Geometry 03E50, 51N20 |
| url | https://arxiv.org/abs/2406.04078 |