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dc.contributor.author | Aliaga, Ramón J. | es_ES |
dc.contributor.author | Gartland, Chris | es_ES |
dc.contributor.author | Petitjean, Colin | es_ES |
dc.contributor.author | Procházka, Antonín | es_ES |
dc.date.accessioned | 2023-09-21T18:06:24Z | |
dc.date.available | 2023-09-21T18:06:24Z | |
dc.date.issued | 2022-05 | es_ES |
dc.identifier.issn | 0002-9947 | es_ES |
dc.identifier.uri | http://hdl.handle.net/10251/196933 | |
dc.description.abstract | [EN] We characterize compact metric spaces whose locally flat Lip-schitz functions separate points uniformly as exactly those that are purely 1-unrectifiable, resolving a problem of Weaver. We subsequently use this geometric characterization to answer several questions in Lipschitz analysis. Notably, it follows that the Lipschitz-free space F(M) over a compact metric space M is a dual space if and only if M is purely 1-unrectifiable. Furthermore, we establish a compact determinacy principle for the Radon-Nikodym property (RNP) and deduce that, for any complete metric space M, pure 1-unrectifiability is actually equivalent to some well-known Banach space properties of F(M) such as the RNP and the Schur property. A direct consequence is that any complete, purely 1-unrectifiable metric space isometrically embeds into a Banach space with the RNP. Finally, we provide a possible solution to a problem of Whitney by finding a rectifiability-based description of 1-critical compact metric spaces, and we use this description to prove the following: a bounded turning tree fails to be 1-critical if and only if each of its subarcs has sigma-finite Hausdorff 1-measure. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | American Mathematical Society | es_ES |
dc.relation.ispartof | Transactions of the American Mathematical Society | es_ES |
dc.rights | Reconocimiento - No comercial (by-nc) | es_ES |
dc.subject | Purely 1-unrectifiable | es_ES |
dc.subject | Radon-Nikodym property | es_ES |
dc.subject | Whitney arc | es_ES |
dc.subject | Lipschitz-free space | es_ES |
dc.subject | Locally flat Lipschitz function | es_ES |
dc.subject.classification | TECNOLOGIA ELECTRONICA | es_ES |
dc.title | Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.1090/tran/8591 | es_ES |
dc.relation.projectID | info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2017-83262-C2-2-P/ES/LA INTERACCION ENTRE GEOMETRIA Y TOPOLOGIA EN ESPACIOS DE BANACH. APLICACIONES/ | es_ES |
dc.rights.accessRights | Abierto | es_ES |
dc.contributor.affiliation | Universitat Politècnica de València. Escuela Técnica Superior de Ingenieros de Telecomunicación - Escola Tècnica Superior d'Enginyers de Telecomunicació | es_ES |
dc.description.bibliographicCitation | Aliaga, RJ.; Gartland, C.; Petitjean, C.; Procházka, A. (2022). Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions. Transactions of the American Mathematical Society. 375(5):3529-3567. https://doi.org/10.1090/tran/8591 | es_ES |
dc.description.accrualMethod | S | es_ES |
dc.relation.publisherversion | https://doi.org/10.1090/tran/8591 | es_ES |
dc.description.upvformatpinicio | 3529 | es_ES |
dc.description.upvformatpfin | 3567 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 375 | es_ES |
dc.description.issue | 5 | es_ES |
dc.relation.pasarela | S\478629 | es_ES |
dc.contributor.funder | Ministerio de Economía, Industria y Competitividad | es_ES |