Minimally almost periodic group topologies on countably infinite Abelian groups

Proceedings of the American Mathematical Society

Volumn 143, Issue 4, 2015, Pages 1823-1829

  Gabriyelyan, S S ^a  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

Author keywords

Countable Abelian group; Dual group; Minimally almost periodic; T sequence; Von Neumann radical

Indexed keywords

EID: 84923241715     PISSN: 00029939     EISSN: 10886826     Source Type: Journal    
DOI: 10.1090/S0002-9939-2014-12383-5     Document Type: Article

References (28)

1. M. Ajtai, I. Havas, and J. Komlós, Every group admits a bad topology, Studies in pure mathematics, Birkhäuser, Basel, 1983, pp. 21-34. MR820207 (86k:22002)
2. Alexander Arhangel'skii and Mikhail Tkachenko, Topological groups and related structures, Atlantis Studies in Mathematics, vol. 1, Atlantis Press, Paris, 2008. MR2433295 (2010i:22001)
3. Giuseppina Barbieri, Dikran Dikranjan, Chiara Milan, and Hans Weber, Answer to Raczkowski's questions on convergent sequences of integers, Topology Appl. 132 (2003), no. 1, 89-101, DOI 10.1016/S0166-8641(02)00366-8. MR1990082 (2004e:54033)
4. Giuseppina Barbieri, Dikran Dikranjan, Chiara Milan, and Hans Weber, Convergent sequences in precompact group topologies, Appl. Gen. Topol. 6 (2005), no. 2, 149-169. MR2195810 (2006k:22001)
5. M. Beiglböck, C. Steineder, and R.Winkler, Sequences and filters of characters characterizing subgroups of compact abelian groups, Topology Appl. 153 (2006), no. 11, 1682-1695, DOI 10.1016/j.topol.2005.06.003. MR2227021 (2008g:43010)
6. W. W. Comfort, Problems on topological groups and other homogeneous spaces, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 313-347. MR1078657
7. p with 0 < p < 1, Bull. Amer. Math. Soc. 46 (1940), 816-823. MR0002700 (2,102b)
8. Dikran Dikranjan and Kenneth Kunen, Characterizing subgroups of compact abelian groups, J. Pure Appl. Algebra 208 (2007), no. 1, 285-291, DOI 10.1016/j.jpaa.2005.12.011. MR2269843 (2008a:22001)
9. Dikran Dikranjan, Chiara Milan, and Alberto Tonolo, A characterization of the maximally almost periodic abelian groups, J. Pure Appl. Algebra 197 (2005), no. 1-3, 23-41, DOI 10.1016/j.jpaa.2004.08.021. MR2123978 (2005m:20003)
10. Dikran Dikranjan and Dmitri Shakhmatov, The Markov-Zariski topology of an abelian group, J. Algebra 324 (2010), no. 6, 1125-1158, DOI 10.1016/j.jalgebra.2010.04.025. MR2671798 (2011i:20078)
11. L. Fuchs, Abelian groups, Publishing House of the Hungarian Academy of Sciences, Budapest, 1958. MR0106942 (21 #5672)
12. S. S. Gabriyelyan, Characterization of almost maximally almost-periodic groups, Topology Appl. 156 (2009), no. 13, 2214-2219, DOI 10.1016/j.topol.2009.05.003. MR2544129 (2010g:20104)
13. S. S. Gabriyelyan, On T-sequences and characterized subgroups, Topology Appl. 157 (2010), no. 18, 2834-2843, DOI 10.1016/j.topol.2010.09.002. MR2729343 (2012a:22010)
14. S. S. Gabriyelyan, Finitely generated subgroups as von Neumann radicals of an Abelian group (English, with English and Russian summaries), Mat. Stud. 38 (2012), no. 2, 124- 138. MR3057998
15. S. S. Gabriyelyan, Bounded subgroups as a von Neumann radical of an Abelian group, Topology Appl. 178 (2014), 185-199.
16. S. S. Gabriyelyan, On characterized subgroups of Abelian topological groups X and the group of all X-valued null sequences, Comment. Math. Univ. Carolin. 55 (2014), no. 1, 73-99.
17. S. S. Gabriyelyan, On T-characterized subgroups of compact Abelian groups, preprint.
18. M. I. Graev, Free topological groups (Russian), Izvestiya Akad. Nauk SSSR. Ser. Mat. 12 (1948), 279-324. MR0025474 (10,11d)
19. Edwin Hewitt and Kenneth A. Ross, Abstract harmonic analysis. Vol. I, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 115, Springer-Verlag, Berlin, 1979. Structure of topological groups, integration theory, group representations. MR551496 (81k:43001)
20. Sidney A. Morris, Pontryagin duality and the structure of locally compact abelian groups, Cambridge University Press, Cambridge, 1977. London Mathematical Society Lecture Note Series, No. 29. MR0442141 (56 #529)
21. J. von Neumann, Almost periodic functions in a group. I, Trans. Amer. Math. Soc. 36 (1934), no. 3, 445-492, DOI 10.2307/1989792. MR1501752
22. J. W. Nienhuys, A solenoidal and monothetic minimally almost periodic group, Fund. Math. 73 (1971/72), no. 2, 167-169. MR0291348 (45 #442)
23. J. W. Nienhuys, Construction of group topologies on abelian groups, Fund. Math. 75 (1972), no. 2, 101-116. (errata insert). MR0302810 (46 #1953)
24. I. Prodanov, Elementary example of a group without characters, In: Mathematics and Mathematical Education, Proc. 9th Spring Conference (April 1980) of the Bulgarian Math. Soc., Bulg. Acad. Sci., Sofia, (1980), 79-81.
25. I. V. Protasov, Review of Ajtai, Havas and J. Komlós[1983], Zentralblatt für Matematik, 535, 93.
26. I. V. Protasov and E. G. Zelenyuk, Topologies on abelian groups (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 5, 1090-1107; English transl., Math. USSR-Izv. 37 (1991), no. 2, 445-460. MR1086087 (93b:22001)
27. I. Protasov and E. Zelenyuk, Topologies on groups determined by sequences, Mathematical Studies Monograph Series, vol. 4, VNTL Publishers, L'viv, 1999. MR1718814 (2001i:22005)
28. D. Remus, Topological groups without nontrivial characters, (Prague, 1986), Res. Exp. Math., vol. 16, Heldermann, Berlin, 1988, pp. 477-484. MR952630 (89f:22002)