Self-duality in the class of precompact groups

Topology and its Applications

Volumn 156, Issue 12, 2009, Pages 2158-2165

  Tkachenko, Mikhail ^a,b  

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

^b UNIVERSITAT JAUME I   (Spain)

Author keywords

Countably compact; Countably pseudocompact; Dual group; MAP group; Precompact; Pseudocompact; Reflexive; Self dual

Indexed keywords

EID: 67349254997     PISSN: 01668641     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.topol.2009.03.039     Document Type: Article

References (20)

1. S. Ardanza-Trevijano, M.J. Chasco, X. Domínguez, M.G. Tkachenko, Precompact non-compact reflexive Abelian groups, submitted for publication
2. Arhangel'skii A.V., and Tkachenko M.G. Topological Groups and Related Structures. Atlantis Studies in Mathematics vol. I (2008), Atlantis Press/World Scientific, Paris/Amsterdam
3. Banaszczyk W. Additive Subgroups of Topological Vector Spaces. Lecture Notes in Math. vol. 1466 (1991), Springer-Verlag, Berlin/Heidelberg
4. Chasco M.J. Pontryagin duality for metrizable groups. Arch. Math. 70 (1998) 22-28
5. Chasco M.J., and Martín-Peinador E. Pontryagin duality and strong duality. Extracta Math. 6 1 (1991) 44-46
6. Chasco M.J., and Martín-Peinador E. On strongly reflexive topological groups. Appl. Gen. Topol. 2 (2001) 219-226
7. Comfort W.W., and Ross K.A. Pseudocompactness and uniform continuity in topological groups. Pacific J. Math. 16 3 (1966) 483-496
8. Corwin L. Some remarks on self-dual locally compact Abelian groups. Trans. Amer. Math. Soc. 148 2 (1970) 613-622
9. Dikranjan D.N., and Shakhmatov D.B. Algebraic structure of pseudocompact groups. Mem. Amer. Math. Soc. 133 633 (1998) 1-83
10. Engelking R. General Topology (1989), Heldermann Verlag, Berlin
11. Hernández S. Pontryagin duality for topological abelian groups. Math. Z. 238 3 (2001) 493-503
12. Hernández S., and Macario S. Dual properties in totally bounded Abelian groups. Arch. Math. (Basel) 80 (2003) 271-283
13. Hernández S., and Uspenskij V. Pontryagin duality for spaces of continuous functions. J. Math. Anal. Appl. 242 (2000) 135-144
14. Hewitt E., and Ross K. Abstract Harmonic Analysis, vol. I (1979), Springer-Verlag, Berlin/Göttingen/Heidelberg
15. Kaplan S. Extensions of the Pontryagin duality I: Infinite products. Duke Math. J. 15 (1948) 649-658
16. Leptin H. Abelsche Gruppen mit kompakten Charaktergruppen und Dualitätstheorie gewisser linear topologischer abelscher Gruppen. Abh. Math. Sem. Univ. Hamburg 19 (1955) 244-263
17. Pestov V.G. Free topological abelian groups and the Pontryagin duality. Moscow Univ. Math. Bull. 41 (1986) 1-4 Russian original in: Vestnik Mosk. Univ. Ser. I (1) 3-5
18. Pestov V.G. Free abelian topological groups and the Pontryagin-van Kampen duality. Bull. Austral. Math. Soc. 52 (1995) 297-311
19. Raczkowski S.U., and Trigos-Arrieta F.J. Duality of totally bounded Abelian groups. Bol. Soc. Mat. Mexicana (3) 7 1 (2001) 1-12
20. Venkataraman R. Extensions of Pontryagin duality. Math. Z. 143 2 (1975) 105-112