Interpolation sets in spaces of continuous metric-valued functions
Scholar | Other documents of the author: Ferrer González, María Vicenta; Hernández Muñoz, Salvador; Tárrega Ruiz, Luis
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TitleInterpolation sets in spaces of continuous metric-valued functions
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. [-]
Investigation projectSpanish Ministerio de Economía y Competitividad, (grant MTM2016-77143-P) ; Universitat Jaume I (grant P1171B2015-77) ; Generalitat Valenciana (grant: PROMETEO/2014/062)
Bibliographic citationFERRER, 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.
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