A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911143041171456 |
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| author | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| author_facet | Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi |
| contents | We provide a geometric proof of the $(\aleph_{0}, d+1)$-theorem for piercing compact connected sets by hyperplanes. Our argument uses only elementary properties of convex sets and clarifies the core geometric structure behind the theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10012 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing Chakraborty, Sutanoya Ghosh, Arijit Nandi, Soumi Combinatorics Computational Geometry 52A35 We provide a geometric proof of the $(\aleph_{0}, d+1)$-theorem for piercing compact connected sets by hyperplanes. Our argument uses only elementary properties of convex sets and clarifies the core geometric structure behind the theorem. |
| title | A geometric proof of the infinite $(p, q)$-theorem for hyperplane piercing |
| topic | Combinatorics Computational Geometry 52A35 |
| url | https://arxiv.org/abs/2402.10012 |