Precompact noncompact reflexive Abelian groups

Forum Mathematicum

Volumn 24, Issue 2, 2012, Pages 289-302

  Ardanza Trevijano, Sergio ^a   Chasco, María Jesús ^a   Domínguez, Xabier ^b   Tkachenko, Mikhail ^c  

^a UNIVERSITY OF NAVARRA   (Spain)

^b UNIVERSITY OF A CORUÑA   (Spain)

^c DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

Countably compact group; H embedded subgroup; Pontryagin dual; Pontryagin reflexive group; Precompact group; Pseudocompact group

Indexed keywords

EID: 84858694152     PISSN: 09337741     EISSN: 14355337     Source Type: Journal    
DOI: 10.1515/FORM.2011.061     Document Type: Review

References (20)

1. A.V. Arhangel'skii and M. G. Tkachenko, Topological Groups and Related Structures, Atlantis Press/World Scientific, Amsterdam, Paris, 2008.
2. L. Außenhofer, Contributions to the Duality Theory of Abelian Topological Groups and to the Theory of Nuclear Groups, Dissertationes Mathematicae 384, 1999.
3. W. Banaszczyk, M. J. Chasco and E. Martín-Peinador, Open subgroups and Pontryagin duality, Math. Z. 215 (1994), no. 2, 195-204.
4. M. J. Chasco, Pontryagin duality for metrizable groups, Arch. Math. 70 (1998), 22-28.
5. M. J. Chasco and E. Martín-Peinador, An approach to duality on Abelian precompact groups, J. Group Theory 11 (2008), 635-643.
6. W.W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283-291.
7. W.W. Comfort and K. A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966), 483-496.
8. D. Dikranjan and D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topol. Appl. 151 (2005), 2-54. (Pubitemid 40651957)
9. D. Dikranjan and M. G. Tkachenko, Sequential completeness of quotient groups, Bull. Austral. Math. Soc. 61 (2000), 129-151.
10. D. Dikranjan and M. G. Tkachenko, Algebraic structure of small countably compact groups, Forum Math. 15 (2003), no. 6, 811-837. (Pubitemid 37353099)
11. R. Engelking, General Topology, Sigma Series in Pure Mathematics 6, Heldermann-Verlag, Berlin, 1989.
12. J. Galindo and S. Macario, Pseudocompact group topologies with no infinite compact subsets, preprint, arXiv:0812.5033v2, January 16, 2009.
13. J. Galindo, L. Recoder and M. Tkachenko, Nondiscrete P-groups can be reflexive, preprint, arXiv:1002.4730v1, February 25, 2010.
14. I. Glicksberg, Uniform boundedness for groups, Can. J. Math. 14 (1962), 269-276.
15. D. L. Grant, Topological groups which satisfy an open mapping theorem, Pacific J. Math. 68 (1977), 411-423.
16. S. Hernández and S. Macario, Dual properties in totally bounded Abelian groups, Archiv der Mathematik 80 (2003), 271-283. (Pubitemid 36688580)
17. S. Kaplan, Extensions of the Pontryagin duality I. Infinite products, Duke Math. J. 15 (1948), 649-658.
18. H. Leptin, Abelsche Gruppen mit kompakten Charaktergruppen und Dualitätstheorie gewisser linear topologischer abelscher Gruppen, Abh. Math. Sem. Univ. Hamburg 19 (1955), 244-263.
19. S. U. Raczkowski and F. J. Trigos-Arrieta, Duality of totally bounded Abelian groups, Bol. Soc. Mat. Mex. III 7 (2001), no. 1, 1-12. (Pubitemid 33574863)
20. M. G. Tkachenko, Compactness type properties in topological groups, Czech. Math. J. 38 (1988), no. 2, 324-341.