On a transversal theorem of Montejano and Karasev
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866929486660894720 |
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| author | Holmsen, Andreas F. |
| author_facet | Holmsen, Andreas F. |
| contents | We give a new proof of a theorem of Montejano and Karasev regarding $k$-dimensional transversals to small families of convex sets. While their proof uses technical algebraic and topological tools, our proof is a simple application of the Borsuk-Ulam theorem. Additionally, in certain cases our result is stronger than the Montejano-Karasev theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_07907 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On a transversal theorem of Montejano and Karasev Holmsen, Andreas F. Combinatorics We give a new proof of a theorem of Montejano and Karasev regarding $k$-dimensional transversals to small families of convex sets. While their proof uses technical algebraic and topological tools, our proof is a simple application of the Borsuk-Ulam theorem. Additionally, in certain cases our result is stronger than the Montejano-Karasev theorem. |
| title | On a transversal theorem of Montejano and Karasev |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2112.07907 |