Interpolation sets in spaces of continuous metric-valued functions
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Otros documentos de la autoría: Ferrer González, María Vicenta; Hernández, Salvador; Tárrega Ruiz, Luis
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Título
Interpolation sets in spaces of continuous metric-valued functionsFecha de publicación
2018-10Editor
ElsevierCita bibliográfica
FERRER, María V.; HERNÁNDEZ, Salvador; TÁRREGA, Luis. Interpolation sets in spaces of continuous metric-valued functions. Journal of Mathematical Analysis and Applications, 2018, 466.2: 1426-1442.Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
https://www.sciencedirect.com/science/article/pii/S0022247X18305444Versión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
Let X and K be a Cech-complete topological group and a compact group, ˇ
respectively. We prove that if G is a non-equicontinuous subset of CHom(X; K), the set
of all continuous homomorphisms of X into K, then there ... [+]
Let X and K be a Cech-complete topological group and a compact group, ˇ
respectively. We prove that if G is a non-equicontinuous subset of CHom(X; K), the set
of all continuous homomorphisms of X into K, then there is a countably infinite subset
L ⊆ G such that LKX is canonically homeomorphic to β!, the Stone-Cech compactifca- ˇ
tion of the natural numbers. As a consequence, if G is an infinite subset of CHom(X; K)
such that for every countable subset L ⊆ G and compact separable subset Y ⊆ X it
holds that either LKY has countable tightness or jLKY j ≤ c, then G is equicontinuous.
Given a topological group G, denote by G+ the (algebraic) group G equipped with the
Bohr topology. It is said that G respects a topological property P when G and G+ have
the same subsets satisfying P. As an application of our main result, we prove that if
G is an abelian, locally quasiconvex, locally k! group, then the following holds: (i) G
respects any compact-like property P stronger than or equal to functional boundedness;
(ii) G strongly respects compactness. [-]
Proyecto de investigación
Spanish Ministerio de Economía y Competitividad, (grant MTM2016-77143-P) ; Universitat Jaume I (grant P1171B2015-77) ; Generalitat Valenciana (grant: PROMETEO/2014/062)Derechos de acceso
© 2018 Elsevier Inc. All rights reserved.
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