Invariance of compactness for the Bohr topology

Topology and its Applications

Volumn 111, Issue 1-2, 2000, Pages 161-173

  Hernández, Salvador ^a   Macario, Sergio ^a  

^a UNIVERSITAT JAUME I   (Spain)

Author keywords

Bohr topology; ech complete group; C* embedded; C embedded; G group; Respects compactness

Indexed keywords

EID: 12744277866     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. A.V. Arhangel'skii, On a class of spaces containing all metric and all locally bicompact spaces, Soviet Math. Dokl. 4 (1963) 1051-1055.
2. L. Außenhofer, Contributions to the duality theory of Abelian topological groups and to the theory of nuclear groups, Doctoral Dissertation, 1998.
3. W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Math., Vol. 1466, Springer, Berlin, 1991.
4. W. Banaszczyk, E. Martín-Peinador, The Glicksberg theorem on weakly compact sets of nuclear groups, in: Papers on General Topology and Applications, Amsterdam, Ann. New York Acad. Sci., Vol. 788, New York, 1994, pp. 34-39.
5. W. Banaszczyk, E. Martín-Peinador, Weakly pseudocompacts subsets of nuclear groups, J. Pure Appl. Algebra 138 (1999) 99-106.
6. N. Bourbaki, Éléments de Mathématique. Topologie Générale, Hermann, Paris, 1971.
7. 1 sequences generated by Sidon sets, J. Eondon Math. Soc. (2) 29 (1984) 283-288.
8. M.J. Chasco, E. Martín-Peinador, V. Tarieladze, On Mackey topology for groups, Preprint, 1997.
9. W.W. Comfort, K.A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964) 283-291.
10. E.K. van Douwen, The maximal totally bounded group topology on G and the biggest minimal G-space for Abelian groups G, Topology Appl. 34 (1990) 69-91.
11. J. Galindo, S. Hernández, The concept of boundedness and the Bohr compactification of a MAP Abelian group, Fund. Math. 159 (1999) 195-218.
12. I. Glicksberg, Uniform boundedness for groups, Canadian J. Math. 14 (1962) 269-276.
13. A. Grothendieck, Sur la complétion du dual d'un space vectoriel localement convexe, C. R. Acad. Sci. Paris 230 (1950) 605-606.
14. A. Grothendieck, Critères de compacité dans les espaces fonctonniels généraux, Amer. J. Math. 74 (1952) 168-186.
15. E. Hewitt, K.A. Ross, Abstract Harmonic Analysis, Vol. I, Grundlehren Math. Wiss. Einzeldarstellungen, Vol. 115, Springer, Berlin, 1963.
16. R.J. Hunter, J. Lloyd, Weakly compactly generated locally convex spaces, Math. Proc. Cambridge Philos. Soc. 82 (1977) 85-98.
17. G. Köthe, Topological Vector Spaces, Vol. I, Grundlehren Math. Wiss. Einzeldarstellungen, Vol. 159, Springer, Berlin, 1969.
18. B.A. Pasynkov, Almost metrizable topological groups, Soviet Math. Dokl. 6 (1965) 404-408.
19. W. Roelcke, S. Dierolf, Uniform Structures on Topological Groups and Their Quotients, McGraw-Hill, New York, 1981.
20. 1, Proc. Nat. Acad. Sci. USA 71 (1974) 2411-2413.
21. I. Singer, Bases in Banach Spaces, II, Springer, Berlin, 1981.
22. F.J. Trigos-Arrieta, Pseudocompactness on groups, Ph.D. Thesis, Wesleyan University, Middletown, CT, 1991.
23. F.J. Trigos-Arrieta, Continuity, boundedness, connectedness and the Lindelöf property for topological groups, J. Pure Appl. Algebra 70 (1991) 199-210.
24. M. Valdivia, Some new results on weak compactness, J. Funct. Anal. 24 (1977) 1-10.