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dc.contributor.author | Cholaquidis, Alejandro | es_ES |
dc.date.accessioned | 2023-05-02T06:40:13Z | |
dc.date.available | 2023-05-02T06:40:13Z | |
dc.date.issued | 2023-04-05 | |
dc.identifier.issn | 1576-9402 | |
dc.identifier.uri | http://hdl.handle.net/10251/193023 | |
dc.description.abstract | [EN] 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 ofr-convex supports of absolutely continuous distributions. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Universitat Politècnica de València | es_ES |
dc.relation.ispartof | Applied General Topology | es_ES |
dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
dc.subject | R-convex set | es_ES |
dc.subject | Locally contractible set | es_ES |
dc.subject | Positive reach | es_ES |
dc.title | A counter example on a Borsuk conjecture | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.4995/agt.2023.18176 | |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Cholaquidis, A. (2023). A counter example on a Borsuk conjecture. Applied General Topology. 24(1):125-128. https://doi.org/10.4995/agt.2023.18176 | es_ES |
dc.description.accrualMethod | OJS | es_ES |
dc.relation.publisherversion | https://doi.org/10.4995/agt.2023.18176 | es_ES |
dc.description.upvformatpinicio | 125 | es_ES |
dc.description.upvformatpfin | 128 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 24 | es_ES |
dc.description.issue | 1 | es_ES |
dc.identifier.eissn | 1989-4147 | |
dc.relation.pasarela | OJS\18176 | es_ES |
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