Publication: Searching for a Debreu’s open gap lemma for semiorders
| dc.contributor.author | Estevan Muguerza, Asier | |
| dc.contributor.department | Estatistika, Informatika eta Matematika | eu |
| dc.contributor.department | Institute for Advanced Materials and Mathematics - INAMAT2 | en |
| dc.contributor.department | Estadística, Informática y Matemáticas | es_ES |
| dc.date.accessioned | 2020-05-29T07:13:38Z | |
| dc.date.available | 2022-01-24T00:00:13Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | In 1956 R. D. Luce introduced the notion of a semiorder to deal with indifference relations in the representation of a preference. During several years the problem of finding a utility function was studied until a representability characterization was found. However, there was almost no results on the continuity of the representation. A similar result to Debreu’s Lemma, but for semiorders was never achieved. In the present paper we propose a characterization for the existence of a continuous representation (in the sense of Scott-Suppes) for bounded semiorders. As a matter of fact, the weaker but more manageable concept of ε-continuity is properly introduced for semiorders. As a consequence of this study, a version of the Debreu’s Open Gap Lemma is presented (but now for the case of semiorders) just as a conjecture, which would allow to remove the open-closed and closed-open gaps of a subset S ⊆ R, but now keeping the constant threshold, so that x + 1 < y if and only if g(x) + 1 < g(y) (x, y ∈ S). | en |
| dc.description.sponsorship | The author acknowledges financial support from the Ministry of Economy and Competitiveness of Spain under grants MTM2015-63608-P and ECO2015-65031. | en |
| dc.embargo.lift | 2022-01-24 | |
| dc.embargo.terms | 2022-01-24 | |
| dc.format.extent | 20 p. | |
| dc.format.mimetype | application/pdf | en |
| dc.identifier.doi | 10.1007/978-3-030-34226-5_5 | |
| dc.identifier.isbn | 978-3-030-34225-8 | |
| dc.identifier.issn | 2198-4182 | |
| dc.identifier.uri | https://academica-e.unavarra.es/handle/2454/36989 | |
| dc.language.iso | eng | en |
| dc.publisher | Springer | en |
| dc.relation.ispartof | Bosi, G., Campión, M., Candeal, J., Indurain, E. (eds.) Mathematical Topics on Representations of Ordered Structures and Utility Theory. Springer: Cham, 2020, pp. 109-128. ISBN 978-3-030-34225-8. | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//MTM2015-63608-P/ES/ | en |
| dc.relation.projectID | info:eu-repo/grantAgreement/MINECO//ECO2015-65031-R/ES/ | en |
| dc.relation.publisherversion | https://doi.org/10.1007/978-3-030-34226-5_5 | |
| dc.rights | © Springer Nature Switzerland AG 2020 | en |
| dc.rights.accessRights | info:eu-repo/semantics/openAccess | en |
| dc.rights.accessRights | Acceso abierto / Sarbide irekia | es |
| dc.subject | Semiorders | en |
| dc.subject | Debreu’s Open Gap Lemma | en |
| dc.title | Searching for a Debreu’s open gap lemma for semiorders | en |
| dc.type | info:eu-repo/semantics/bookPart | en |
| dc.type | Capítulo de libro / Liburuen kapitulua | es |
| dc.type.version | info:eu-repo/semantics/acceptedVersion | en |
| dc.type.version | Versión aceptada / Onetsi den bertsioa | es |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e442a64a-b62e-4338-9a67-d7f4d9f12813 | |
| relation.isAuthorOfPublication.latestForDiscovery | e442a64a-b62e-4338-9a67-d7f4d9f12813 |