Bounded subgroups as a von Neumann radical of an Abelian group

Topology and its Applications

Volumn 178, Issue , 2014, Pages 185-199

  Gabriyelyan, S S ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Abelian group; Bounded Abelian group; Dual group; T sequence; Von Neumann radical

Indexed keywords

EID: 84907795720     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2014.09.007     Document Type: Article

References (26)

1. Ajtai M., Havas I., Komlós J. Every group admits a bad topology. Stud. Pure Math. 1983, 21-34. Birkhäuser, Basel and Boston, Memory of P. Turan.
2. Banaszczyk W. Additive Subgroups of Topological Vector Spaces. Lecture Notes in Mathematics 1991, vol. 1466. Springer, Berlin-Heidelberg-New York.
3. Comfort W.W. Problems on topological groups and other homogeneous spaces. Open Problems in Topology 1990, 314-347. North-Holland.
4. p with 0
5. Dikranjan D., Milan C., Tonolo A. A characterization of the maximally almost periodic Abelian groups. J. Pure Appl. Algebra 2005, 197:23-41.
6. Fuchs L. Abelian Groups 1967, Publishing House of the Hungarian Academy of Sciences, Budapest, Pergamon Press, London. third edition, reprinted.
7. Gabriyelyan S.S. Characterization of almost maximally almost-periodic groups. Topol. Appl. 2009, 156:2214-2219.
8. Gabriyelyan S.S. On T-sequences and characterized subgroups. Topol. Appl. 2010, 157:2834-2843.
9. Gabriyelyan S.S. Finitely generated subgroups as a von Neumann radical of an Abelian group. Mat. Stud. 2012, 38:124-138.
10. Gabriyelyan S.S. On extensions of bounded subgroups in Abelian groups. Comment. Math. Univ. Carol. 2014, 55:175-188.
11. Gabriyelyan S.S. Minimally almost periodic group topologies on countably infinite Abelian groups. Proc. Am. Math. Soc. 2014, in press.
12. Gabriyelyan S.S. On characterized subgroups of Abelian topological groups X and the group of all X-valued null sequences. Comment. Math. Univ. Carol. 2014, 50:73-99.
13. S.S. Gabriyelyan, On T-characterized subgroups of compact Abelian groups, submitted for publication.
14. Halmos P.R. Comment on the real line. Bull. Am. Math. Soc. 1944, 50:877-878.
15. Hewitt E., Ross K.A. Abstract Harmonic Analysis, vol. I 1979, Springer-Verlag, Berlin. 2nd ed.
16. Kaplan S. Extensions of the Pontrjagin duality I: infinite products. Duke Math. J. 1948, 15:649-658.
17. Morris Sidney A. Pontryagin Duality and the Structure of Locally Compact Abelian Groups. London Mathematical Society Lecture Note Series 1977, vol. 29. Cambridge University Press, London.
18. von Neumann J. Almost periodic functions in a group. Trans. Am. Math. Soc. 1934, 36:445-492.
19. Nienhuys J.W. A solenoidal and monothetic minimally almost periodic group. Fundam. Math. 1971, 73:167-169.
20. Nienhuys J.W. Constructions of group topologies on abelian groups. Fundam. Math. 1972, 75:101-116.
21. Noble N. k-Groups and duality. Trans. Am. Math. Soc. 1970, 151:551-561.
22. Prodanov I. Elementary example of a group without characters. Mathematics and Mathematical Education, Proc. 9th Spring Conference of the Bulgarian Math. Soc., Bulg. Acad. Sci. 1980, 79-81.
23. Protasov I.V. Review of Ajtai, Havas and J. Komlós. Zent.bl. Math. 1983, 535:93.
24. Protasov I.V., Zelenyuk E.G. Topologies on abelian groups. Math. USSR, Izv. 1991, 37:445-460. Russian original: Izv. Akad. Nauk SSSR 54, 1090-1107 (1990).
25. Protasov I.V., Zelenyuk E.G. Topologies on Groups Determined by Sequences. Mathematical Studies: Monograph Series 1999, VNTL, Lviv.
26. Zelenyuk Y. Metrizable refinements of group topologies and the pseudo-intersection number. Topol. Appl. 2011, 158:1172-1178.