Complete invariant fuzzy metrics on groups
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https://doi.org/10.1016/j.fss.2016.12.019 |
Metadata
Title
Complete invariant fuzzy metrics on groupsDate
2018-01-01Publisher
ElsevierBibliographic citation
SÁNCHEZ, Iván; SANCHIS LÓPEZ, Manuel. (2018). Complete invariant fuzzy metrics on groups. Fuzzy Sets and Systems, v. 330, p. 41-51Type
info:eu-repo/semantics/articlePublisher version
https://www.sciencedirect.com/science/article/pii/S0165011417300015Version
info:eu-repo/semantics/publishedVersionSubject
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 ... [+]
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. [-]
Is part of
Fuzzy Sets and Systems (2018), v. 330Investigation project
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 P1-1B2014-35Rights
http://rightsstatements.org/vocab/CNE/1.0/
info:eu-repo/semantics/restrictedAccess
info:eu-repo/semantics/restrictedAccess
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- IMAC_Articles [122]
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