Borsuk Number for Planar Convex Bodies
By using some simple tools from graph theory, we obtain a characterization of the compact sets in Rn with Borsuk number equal to two. This result allows to give some examples of planar (convex) compact sets with Borsuk number equal to three. Moreover, we also prove that the unique centrally symmetri...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/153990 |
| Acceso en línea: | https://hdl.handle.net/11441/153990 https://doi.org/10.1007/s00025-019-1135-3 |
| Access Level: | acceso abierto |
| Palabra clave: | Borsuk’s question Borsuk number Planar convex bodies Central symmetry Diameter graph |
| Sumario: | By using some simple tools from graph theory, we obtain a characterization of the compact sets in Rn with Borsuk number equal to two. This result allows to give some examples of planar (convex) compact sets with Borsuk number equal to three. Moreover, we also prove that the unique centrally symmetric planar convex compact sets with Borsuk number equal to three are the Euclidean balls. |
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