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Complete invariant fuzzy metrics on groups
dc.contributor.author | Sánchez, Iván | |
dc.contributor.author | Sanchis López, Manuel | |
dc.date.accessioned | 2018-05-14T06:54:08Z | |
dc.date.available | 2018-05-14T06:54:08Z | |
dc.date.issued | 2018-01-01 | |
dc.identifier.citation | SÁNCHEZ, Iván; SANCHIS LÓPEZ, Manuel. (2018). Complete invariant fuzzy metrics on groups. Fuzzy Sets and Systems, v. 330, p. 41-51 | ca_CA |
dc.identifier.uri | http://hdl.handle.net/10234/174653 | |
dc.description.abstract | We study some questions related to complete fuzzy metric topological groups (in the sense of Kramosil and Michael). Invariant fuzzy metrics are characterized and we prove that if (G, M, ∗) is a fuzzy metric group such that (M, ∗) is invariant, then a fuzzy metric completion ( ˜ G, ˜ M, ∗) of (G, M, ∗) is a fuzzy metric group and ( ˜ M, ∗) is invariant. Moreover if ( ˜ M, ∗) is an invariant complete metric on (G, τ), then every compatible left invariant (or right invariant) fuzzy metric on G is complete. We also study the so-called three spaces problem: given a fuzzy metric group (G, M, ∗) and a closed normal subgroup N, if one has information about two complete fuzzy metric groups (G, M, ∗), (N, M, ∗) and (G/N, M, ∗), what can be said about the third one. Our results apply to fuzzy Banach spaces. | ca_CA |
dc.format.extent | 11 p. | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | Elsevier | ca_CA |
dc.relation.isPartOf | Fuzzy Sets and Systems (2018), v. 330 | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/CNE/1.0/ | * |
dc.subject | (Complete) Fuzzy metric space | ca_CA |
dc.subject | (Complete) Fuzzy metric topological group | ca_CA |
dc.subject | Invariant fuzzy metric | ca_CA |
dc.subject | Completion of a fuzzy metric topological group | ca_CA |
dc.subject | Quotients of fuzzy metric (normed) spaces | ca_CA |
dc.subject | Three spaces problem | ca_CA |
dc.title | Complete invariant fuzzy metrics on groups | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1016/j.fss.2016.12.019 | |
dc.relation.projectID | 1)The first author is supported by CONACYT of Mexico (Grant number 259783); 2) The second author is supported by the Spanish Ministerio de Economíıa y Competitividad (Grant MTM2016-77143-P), Generalitat Valenciana (Grant AICO/2016/030) and Universitat Jaume I (Grant P1-1B2014-35 | ca_CA |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | ca_CA |
dc.relation.publisherVersion | https://www.sciencedirect.com/science/article/pii/S0165011417300015 | ca_CA |
dc.type.version | info:eu-repo/semantics/publishedVersion | ca_CA |
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