Pontryagin duality in the class of precompact Abelian groups and the Baire property

Journal of Pure and Applied Algebra

Volumn 216, Issue 12, 2012, Pages 2636-2647

  Bruguera, M ^a   Tkachenko, M ^b  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84863110723     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jpaa.2012.03.035     Document Type: Article

References (41)

1. Ardanza-Trevijano S., Chasco M.J., Domínguez X., Tkachenko M.G. Precompact non-compact reflexive Abelian groups. Forum Math. 2012, 24(2):289-302.
2. Arhangel'skii A.V. Relations among the invariants of topological groups and their subspaces. Russian Math. Surveys 1980, 35:1-23. Russian original in: Uspekhy Mat. Nauk 35 (1980) 3-22.
3. Arhangel'skii A.V., Tkachenko M.G. Topological Groups and Related Structures. Atlantis Studies in Mathematics 2008, vol.~I. Atlantis Press and World Scientific, Paris, Amsterdam.
4. 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.
5. Banaszczyk W. Additive Subgroups of Topological Vector Spaces. Lecture Notes in Math. 1991, vol.~1466. Springer Verlag, Berlin, Heidelberg.
6. Banaszczyk W., Chasco M.J., Martín-Peinador E. Open subgroups and Pontryagin duality. Math. Z. 1994, 215(2):195-204.
7. N. Bourbaki, Elements of Mathematics. General Topology. PartI, Paris, 1966.
8. Chasco M.J. Pontryagin duality for metrizable groups. Arch. Math. 1998, 70(1):22-28.
9. Chasco M.J., Martín-Peinador E. An approach to duality on Abelian precompact groups. J. Group Theory 2008, 11:635-643.
10. Chasco M.J., Martín-Peinador E., Tarieladze V. On Mackey topology for groups. Studia Math. 1999, 132(3):257-262.
11. Cohen P.E. Products of Baire spaces. Proc. Amer. Math. Soc. 1976, 55:119-124.
12. Comfort W.W., Raczkowski S.U., Trigos-Arrieta F.J. The dual group of a dense subgroup. Czech. Math. J. 2004, 54(2):509-533.
13. Comfort W.W., Ross K.A. Topologies induced by groups of character. Fund. Math. 1964, 55:283-291.
14. Comfort W.W., Ross K.A. Pseudocompactness and uniform continuity in topological groups. Pacific J. Math. 1966, 16(3):483-496.
15. Dikranjan D., Shakhmatov D.B. Quasi-convex density and determining subgroups of compact abelian groups. J. Math. Anal. Appl. 2010, 363(1):42-48.
16. Dikranjan D., Tkachenko M.G. Sequential completeness of quotient groups. Bull. Austral. Math. Soc. 2000, 61:129-151.
17. Engelking R. General Topology 1989, Heldermann Verlag, Berlin.
18. Fleischer I., Traynor T. Continuity of homomorphisms on a Baire group. Proc. Amer. Math. Soc. 1985, 93(2):367-368.
19. Fleissner W., Kunen K. Barely Baire spaces. Fund. Math. 1978, 101(3):229-240.
20. Fuchs L. Infinite Abelian Groups I. Pure and Applied Mathematics 1970, vol. 36. Academic Press.
21. Galindo J., García-Ferreira S. Compact groups containing dense pseudocompact subgroups without non-trivial convergent sequences. Topol. Appl. 2007, 154(2):476-490.
22. Galindo J., Hernández S. Pontryagin-van Kampen reflexivity for free Abelian topological groups. Forum Math. 1999, 11(4):399-415.
23. Galindo J., Macario S. Pseudocompact group topologies with no infinite compact subsets. J. Pure Appl. Algebra 2011, 215(4):655-663.
24. Guran I. On topological groups close to being Lindelöf. Soviet Math. Dokl. 1981, 23:173-175. Russian original in: Dokl. Acad. Nauk SSSR 256 (1981) 1035-1037.
25. Hernández S., Macario S. Dual properties in totally bounded abelian groups. Arch. Math. (Basel) 2003, 80(3):271-283.
26. Hewitt E., Ross K.A. Abstract Harmonic Analysis, Volume I 1979, Springer-Verlag, Berlin, Göttingen, Heidelberg.
27. Kaplan S. Extension of the Pontryagin duality I: Infinite products. Duke Math. J. 1948, 15:649-658.
28. Kaplan S. Extensions of the Pontryagin duality. II. Direct and inverse sequences. Duke Math. J. 1950, 17:419-435.
29. Komura Y. Some examples on linear topological spaces. Math. Ann. 1984, 153:150-162.
30. Menini C., Orsatti A. Dualities between categories of topological modules. Comm. Algebra 1983, 11(1):21-66.
31. van Mill J., Pol R. The Baire category theorem in products of linear spaces and topological groups. Topol. Appl. 1986, 22:267-282.
32. Noble N. k-groups and duality. Trans. Amer. Math. Soc. 1970, 151:551-561.
33. Oxtoby J. Cartesian products of Baire spaces. Fund. Math. 1961, 49:157-161.
34. Pasynkov B.A. Almost metrizable topological groups. Dokl. AN SSSR 1965, 161:281-284. (in Russian).
35. Pestov V.G. Free abelian topological groups and the Pontryagin-van~Kampen duality. Bull. Austral. Math. Soc. 1995, 52:297-311.
36. Raczkowski S.U., Trigos-Arrieta F.J. Duality of totally bounded Abelian groups. Bol. Soc. Mat. Mex. III 2001, Ser.~7(1):1-12.
37. Robinson D.J.F. A Course in the Theory of Groups 1982, Springer-Verlag, Berlin.
38. Tkachenko M.G. Compactness type properties in topological groups. Czech. Math. J. 1988, 38(2):324-341.
39. Valdivia M. Products of Baire topological vector spaces. Fund. Math. 1985, 125(1):71-80.
40. Venkataraman R. Extensions of Pontryagin duality. Math. Z. 1975, 143(2):105-112.
41. Vilenkin N.Ya. Theory of weakly separable topological groups. Mat. Sb. 1948, 22:135-177. (in Russian).