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Campo DC | Valor | Lengua/Idioma |
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dc.contributor.author | Cholaquidis, Alejandro | - |
dc.date.accessioned | 2023-06-02T14:26:16Z | - |
dc.date.available | 2023-06-02T14:26:16Z | - |
dc.date.issued | 2023 | - |
dc.identifier.citation | Cholaquidis, A. " A counter example on a Borsuk conjecture". Applied General Topology. [en línea] 2023, 24(1): 125-128. 4 h. | es |
dc.identifier.issn | 1989-4147 | - |
dc.identifier.uri | https://hdl.handle.net/20.500.12008/37374 | - |
dc.description.abstract | The study of shape restrictions of subsets of Rd has several applications in many areas, being convexity, r-convexity, and positive reach, some of the most famous, and typically imposed in set estimation. The following problem was attributed to K. Borsuk, by J. Perkal in 1956: find an r-convex set which is not locally contractible. Stated in that way is trivial to find such a set. However, if we ask the set to be equal to the closure of its interior (a condition fulfilled for instance if the set is the support of a probability distribution absolutely continuous with respect to the d-dimensional Lebesgue measure), the problem is much more difficult. We present a counter example of a not locally contractible set, which is r-convex. This also proves that the class of supports with positive reach of absolutely continuous distributions includes strictly the class of r-convex supports of absolutely continuous distributions. | es |
dc.description.sponsorship | ANII: FCE_1_2019_1_156054 | es |
dc.format.extent | 4 h | es |
dc.format.mimetype | application/pdf | es |
dc.language.iso | en | es |
dc.publisher | Universitat Politècnica de València | es |
dc.relation.ispartof | Applied General Topology, 2023, 24(1): 125-128 | es |
dc.rights | Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014) | es |
dc.subject | r-convex set | es |
dc.subject | Locally contractible set | es |
dc.subject | Positive reach | es |
dc.title | A counter example on a Borsuk conjecture | es |
dc.type | Artículo | es |
dc.contributor.filiacion | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. | - |
dc.rights.licence | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) | es |
dc.identifier.doi | 10.4995/agt.2023.18176 | - |
Aparece en las colecciones: | Publicaciones académicas y científicas - Facultad de Ciencias |
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10.4995agt.2023.18176 .pdf | 271,8 kB | Adobe PDF | Visualizar/Abrir |
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