Nondiscrete P-groups can be reflexive

Topology and its Applications

Volumn 158, Issue 2, 2011, Pages 194-203

  Galindo, Jorge ^a   Recoder Núñez, Luis ^b   Tkachenko, Mikhail ^c  

^a UNIVERSITAT JAUME I   (Spain)

^b CENTRAL CONNECTICUT STATE UNIVERSITY   (United States)

^c DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

product; bounded; Character depends on countably many coordinates; Compact subset; P group; Pontryagin's duality; Product; Reflexive

Indexed keywords

EID: 78649634044     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2010.10.015     Document Type: Article

References (16)

1. Ardanza-Trevijano S., Chasco M.J., Domínguez X., Tkachenko M.G. Precompact noncompact reflexive abelian groups preprint, available at. http://arxiv.org/pdf/1001.4895v1.
2. Arhangel'skii A.V., Tkachenko M.G. Topological Groups and Related Structures. Atlantis Ser. Math. 2008, vol. I. Atlantis Press/World Scientific, Paris, Amsterdam.
3. L. Außenhofer, Contributions to the duality theory of Abelian topological groups and to the theory of nuclear groups, PhD dissertation (Der Mathematischen Fakultät der Eberhard-Karls-Universität Tübingen zur Erlangung des Grades eines Doktors der Naturwissenscheaften), 1998.
4. Banaszczyk W. On the existence of exotic Banach-Lie groups. Ann. of Math. 1983, 264:485-493.
5. Banaszczyk W. Additive Subgroups of Topological Vector Spaces 1991, Springer-Verlag, Berlin.
6. Banaszczyk W., Chasco M.J., Martín-Peinador E. Open subgroups and Pontryagin duality. Math. Z. 1994, 215:195-204.
7. M. Bruguera, J. Galindo, C. Hernández, M. Tkachenko, Extensions of reflexive P-groups, preprint.
8. Chasco M.J., Martín-Peinador E. An approach to duality on abelian precompact groups. J. Group Theory 2008, 11(5):635-643.
9. Comfort W.W., Ross K.A. Topologies induced by groups of characters. Fund. Math. 1964, 55:283-291.
10. Galindo J., Macario S. Pseudocompact group topologies with no infinite compact subsets preprint, available at, J. Pure Appl. Algebra, doi:10.1016/j.jpaa.2010.06.014, in press. http://arxiv.org/abs/0812.5033.
11. J. Galindo, L. Recoder-Núñez, M. Tkachenko, Reflexivity of topological groups and P-modification, preprint.
12. Hofmann K.-H., Morris S.A. The Lie Theory of Connected pro-Lie Groups. EMS Tracts Math. 2007, vol. 2. European Math. Soc. (EMS), Zürich.
13. Hofmann K.-H., Morris S.A. Contributions to the structure theory of connected pro-Lie groups. Topology Proc. 2009, 33(4):225-237.
14. Kaplan S. Extension of the Pontryagin duality I: Infinite products. Duke Math. J. 1948, 15:649-658.
15. Leptin H. Zur Dualitätstheorie projektiver Limites abelscher Gruppen. Abh. Math. Sem. Univ. Hamburg 1955, 19:264-268.
16. Noble N. k-groups and duality. Trans. Amer. Math. Soc. 1970, 151:551-561.