On convergent sequences in dual groups
![Thumbnail](/xmlui/bitstream/handle/10234/187579/69347.pdf.jpg?sequence=4&isAllowed=y)
Visualitza/
Impacte
![Google Scholar](/xmlui/themes/Mirage2/images/uji/logo_google.png)
![Microsoft Academico](/xmlui/themes/Mirage2/images/uji/logo_microsoft.png)
Metadades
Mostra el registre complet de l'elementcomunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONMetadades
Títol
On convergent sequences in dual groupsData de publicació
2020-01-16Editor
Real Academia de Ciencias Exactas, Físicas y NaturalesISSN
1578-7303; 1579-1505Cita bibliogràfica
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. 1-10Tipus de document
info:eu-repo/semantics/articleVersió de l'editorial
https://link.springer.com/article/10.1007/s13398-020-00790-xVersió
info:eu-repo/semantics/acceptedVersionParaules clau / Matèries
Resum
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 [-]
Publicat a
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2020, vol. 114, núm. 2, p. 1-10Proyecto de investigación
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).Drets d'accés
"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".
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/openAccess
Apareix a les col.leccions
- INIT_Articles [752]
- MAT_Articles [765]