On convergent sequences in dual groups
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Other documents of the author: Ferrer González, María Vicenta; Hernández, Salvador; Tkachenko, M.
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comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
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Title
On convergent sequences in dual groupsDate
2020-01-16Publisher
Real Academia de Ciencias Exactas, Físicas y NaturalesISSN
1578-7303; 1579-1505Bibliographic citation
FERRER, M. V.; HERNÁNDEZ, S.; TKACHENKO, M. On convergent sequences in dual groups. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, vol. 114, núm. 2, p. 1-10Type
info:eu-repo/semantics/articlePublisher version
https://link.springer.com/article/10.1007/s13398-020-00790-xVersion
info:eu-repo/semantics/acceptedVersionSubject
Abstract
We provide some characterizations of precompact abelian groups G
whose dual group G∧
p
endowed with the pointwise convergence topology on elements of G contains a nontrivial convergent sequence. In
the special ... [+]
We provide some characterizations of precompact abelian groups G
whose dual group G∧
p
endowed with the pointwise convergence topology on elements of G contains a nontrivial convergent sequence. In
the special case of precompact abelian torsion groups G, we characterize the existence of a nontrivial convergent sequence in G∧
p by the
following property of G: No infinite Hausdorff quotient group of G is
countable. Also, we present an example of a dense subgroup G of the
compact metrizable group Z(2)ω
such that G is of the first category
in itself, has measure zero, but the dual group G∧
p does not contain
infinite compact subsets. This complements a result of J.E. Hart and
K. Kunen (2005) on convergent sequences in dual groups. Making use
of the group G we construct the first example of a precompact Pontryagin reflexive abelian group which is of the first Baire category [-]
Is part of
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, vol. 114, núm. 2, p. 1-10Investigation project
M. V. Ferrer was partially supported by the Generalitat Valenciana, Grant GV/2018/110. S. Hernández was partially supported by the Spanish Ministerio de Economía y Competitividad, Grant MTM2016-77143-P (AEI/FEDER, EU).Rights
"This is a post-peer-review, pre-copyedit version of an article published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. The final authenticated version is available online at: https://doi.org/10.1007/s13398-020-00790-x".
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