Complete invariant fuzzy metrics on groups
Metadatos
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https://doi.org/10.1016/j.fss.2016.12.019 |
Metadatos
Título
Complete invariant fuzzy metrics on groupsFecha de publicación
2018-01-01Editor
ElsevierCita bibliográfica
SÁNCHEZ, Iván; SANCHIS LÓPEZ, Manuel. (2018). Complete invariant fuzzy metrics on groups. Fuzzy Sets and Systems, v. 330, p. 41-51Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0165011417300015Versión
info:eu-repo/semantics/publishedVersionPalabras clave / Materias
Resumen
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. [-]
Publicado en
Fuzzy Sets and Systems (2018), v. 330Proyecto de investigación
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 P1-1B2014-35Derechos de acceso
http://rightsstatements.org/vocab/CNE/1.0/
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info:eu-repo/semantics/restrictedAccess
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