Quasi-convex sequences in the circle and the 3-adic integers

Topology and its Applications

Volumn 157, Issue 8, 2010, Pages 1357-1369

  Dikranjan, D ^a   Lukács, Gábor ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSITY OF MANITOBA   (Canada)

Author keywords

3 Adic integers; Qc dense sets; Quasi convex sets; Torus group

Indexed keywords

EID: 77951629343     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2009.04.067     Document Type: Article

References (13)

1. Aussenhofer L. Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups. Dissertationes Math. (Rozprawy Mat.) 1999, 384:113.
2. Banaszczyk W. Additive Subgroups of Topological Vector Spaces. Lecture Notes in Math. 1991, vol. 1466. Springer-Verlag, Berlin.
3. M. Beiglböck, L. de Leo, D. Dikranjan, C. Steineder, On quasi-convexity of finite sets, preprint, March 2005.
4. M. Bruguera, Grupos topológicos y grupos de convergencia: Estudio de la dualidad de Pontryagin, PhD thesis, Universidad Complutense de Madrid, 1999.
5. Bruguera M., Martín-Peinador E. Banach-Dieudonné theorem revisited. J. Aust. Math. Soc. 2003, 75(1):69-83.
6. Chasco M.J., Martín-Peinador E., Tarieladze V. On Mackey topology for groups. Studia Math. 1999, 132(3):257-284.
7. Dikranjan D., Kunen K. Characterizing subgroups of compact abelian groups. J. Pure Appl. Algebra 2007, 208:285-291.
8. Dikranjan D., de Leo L. Countably infinite quasi-convex sets in some locally compact abelian groups. Topology Appl. 2010, 157(8):1347-1356.
9. Dikranjan D., Lukács G. Locally compact abelian groups admitting non-trivial quasi-convex null sequences J. Pure Appl. Algebra, in press. arxiv:/0901.0132.
10. Hernández S. Pontryagin duality for topological abelian groups. Math. Z. 2001, 238(3):493-503.
11. L. de Leo, Weak and strong topologies in topological abelian groups, PhD thesis, Universidad Complutense de Madrid, April 2008, ISBN 978-84-692-1017-8. Colección Digital Tesis UCM, http://eprints.ucm.es/8462/1/T30642.pdf.
12. Lukács G. Notes on Duality Theories of Abelian Groups 2006, Dalhousie University, Chapter I. arxiv:/math.GN/0605149.
13. Vilenkin N.Y. The theory of characters of topological Abelian groups with boundedness given. Izv. Akad. Nauk SSSR Ser. Mat. 1951, 15:439-462.