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Título: | A counter example on a Borsuk conjecture |
Autor: | Cholaquidis, Alejandro |
Tipo: | Artículo |
Palabras clave: | r-convex set, Locally contractible set, Positive reach |
Fecha de publicación: | 2023 |
Resumen: | 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. |
Editorial: | Universitat Politècnica de València |
EN: | Applied General Topology, 2023, 24(1): 125-128 |
Financiadores: | ANII: FCE_1_2019_1_156054 |
DOI: | 10.4995/agt.2023.18176 |
ISSN: | 1989-4147 |
Citación: | Cholaquidis, A. " A counter example on a Borsuk conjecture". Applied General Topology. [en línea] 2023, 24(1): 125-128. 4 h. |
Licencia: | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
Aparece en las colecciones: | Publicaciones académicas y científicas - Facultad de Ciencias |
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