A counter example on a Borsuk conjecture
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 w...
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| Formato: | article |
| Lenguaje: | inglés |
| Publicado: |
2023
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| Materias: | |
| Acceso en línea: | https://hdl.handle.net/20.500.12008/37374 |
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| _version_ | 1868889955692969984 |
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| author | Cholaquidis, Alejandro |
| author_browse | Cholaquidis, Alejandro |
| author_facet | Cholaquidis, Alejandro |
| author_role | author |
| collection | COLIBRI |
| dc.contributor.none.fl_str_mv | Cholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. |
| dc.creator.none.fl_str_mv | Cholaquidis, Alejandro |
| dc.date.none.fl_str_mv | 2023-06-02T14:26:16Z 2023-06-02T14:26:16Z 2023 |
| dc.format.none.fl_str_mv | 4 h application/pdf |
| dc.identifier.none.fl_str_mv | Cholaquidis, A. " A counter example on a Borsuk conjecture". Applied General Topology. [en línea] 2023, 24(1): 125-128. 4 h. 1989-4147 https://hdl.handle.net/20.500.12008/37374 10.4995/agt.2023.18176 |
| dc.language.none.fl_str_mv | en eng |
| dc.publisher.none.fl_str_mv | Universitat Politècnica de València |
| dc.relation.none.fl_str_mv | Applied General Topology, 2023, 24(1): 125-128 |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.none.fl_str_mv | r-convex set Locally contractible set Positive reach |
| dc.title.none.fl_str_mv | A counter example on a Borsuk conjecture |
| dc.type.none.fl_str_mv | Artículo info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | anni_0fa5907d15e510dea0a96c8a2d7d4153 |
| identifier_str_mv | Cholaquidis, A. " A counter example on a Borsuk conjecture". Applied General Topology. [en línea] 2023, 24(1): 125-128. 4 h. 1989-4147 10.4995/agt.2023.18176 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | anni |
| network_name_str | oai-lr-anni |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/37374 |
| publishDate | 2023 |
| publishDateSort | 2023 |
| publisher.none.fl_str_mv | Universitat Politècnica de València |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | A counter example on a Borsuk conjectureCholaquidis, Alejandror-convex setLocally contractible setPositive reachThe 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.ANII: FCE_1_2019_1_156054Universitat Politècnica de ValènciaCholaquidis Alejandro, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.2023-06-02T14:26:16Z2023-06-02T14:26:16Z2023Artículoinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersion4 happlication/pdfCholaquidis, A. " A counter example on a Borsuk conjecture". Applied General Topology. [en línea] 2023, 24(1): 125-128. 4 h.1989-4147https://hdl.handle.net/20.500.12008/3737410.4995/agt.2023.18176reponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaenengApplied General Topology, 2023, 24(1): 125-128Las 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)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)oai:colibri.udelar.edu.uy:20.500.12008/373742026-04-14T10:10:05Z |
| spellingShingle | A counter example on a Borsuk conjecture Cholaquidis, Alejandro r-convex set Locally contractible set Positive reach |
| status_str | publishedVersion |
| title | A counter example on a Borsuk conjecture |
| title_full | A counter example on a Borsuk conjecture |
| title_fullStr | A counter example on a Borsuk conjecture |
| title_full_unstemmed | A counter example on a Borsuk conjecture |
| title_short | A counter example on a Borsuk conjecture |
| title_sort | A counter example on a Borsuk conjecture |
| topic | r-convex set Locally contractible set Positive reach |
| url | https://hdl.handle.net/20.500.12008/37374 |