A countable free closed non-reflexive subgroup of Zc
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Otros documentos de la autoría: Ferrer González, María Vicenta; Hernández, Salvador; Shakhmatov, Dmitry
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Título
A countable free closed non-reflexive subgroup of ZcFecha de publicación
2017Editor
American Mathematical SocietyISSN
0002-9939; 1088-6826Tipo de documento
info:eu-repo/semantics/articleVersión de la editorial
http://www.ams.org/journals/proc/2017-145-08/S0002-9939-2017-13532-1/Versión
info:eu-repo/semantics/submittedVersionPalabras clave / Materias
Resumen
We prove that the group G = Hom(ZN, Z) of all homomorphisms
from the Baer-Specker group ZN to the group Z of integer numbers endowed
with the topology of pointwise convergence contains no infinite compact subsets.
We ... [+]
We prove that the group G = Hom(ZN, Z) of all homomorphisms
from the Baer-Specker group ZN to the group Z of integer numbers endowed
with the topology of pointwise convergence contains no infinite compact subsets.
We deduce from this fact that the second Pontryagin dual of G is discrete.
As G is non-discrete, it is not reflexive. Since G can be viewed as a closed
subgroup of the Tychonoff product Zc of continuum many copies of the integers
Z, this provides an example of a group described in the title, thereby
resolving a problem by Galindo, Recoder-N´u˜nez and Tkachenko. It follows
that an inverse limit of finitely generated (torsion-)free discrete abelian groups
need not be reflexive. [-]
Publicado en
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 145, Number 8, August 2017,Proyecto de investigación
MTM2016-77143-P ; P1·1B2015-77Derechos de acceso
"First published in Proc. Amer. Math. Soc. 145 (2017), published by The American Mathematical Society. (c) 2017 American Mathematical Society."
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