Essential subgroups of topological groups

Communications in Algebra

Volumn 28, Issue 10, 2000, Pages 4941-4970

  Boschi, Elena ^a   Dikranjan, Dikran ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

Essential subgroup; Locally compact group; Pontryagin duality; Totally dense subgroup

Indexed keywords

EID: 0034404405     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927870008827133     Document Type: Article

References (38)

1. A. V. ARHANGEL'SKII, Cardinal invariants of topological groups, embeddings and condensations, Dokl. Acad. Nauk. SSSR 247 (1979), 779-782 (in russian; english translation: Soviet Math.)
2. B. BANASCHEWSKI, Minimal topological algebras, Math. Ann. 211 (1974), 107-114
3. E. BOSCHI and D. DIKRANJAN, Topological groups with totally suitable sets. Preprint
4. W. W. COMFORT, Topological groups, In: Handbook of Set-theoretic Topology, K. Kunen and J. E. Vaughan, editors, Chapter 24, pages 1143-1263. North-Holland, Amsterdam 1984
5. W. COMFORT and D. DIKRANJAN, Essential density and total density in topological groups, 1999 Summer Conference on Topology and its Applications August 4 - 7, 1999 C.W. Post Campus of Long Island University Brookville, NY 11548, USA, Abstracts
6. W.W. COMFORT AND D.L. GRANT, Cardinal invariants, pseudocompactness and minimality: some recent advances in the topological theory of topological groups, Topology Proc. 6 (1981), 227-265
7. COMFORT, W. W., AND LEWIS C. ROBERTSON, Cardinality constraints for pseudocompact and for totally dense subgroups of compact topological groups, Pacific J. Math. 119 (1985), 265-285
8. D. DIKRANJAN, Density and total density of the torsion part of a compact group, Rend. Accad. Naz. dei XL, Memorie di Mat. 108, Vol. XIV, fasc. 13 (1990) 235-252
9. D. DIKRANJAN, Zero-dimensionality of some pseudocompact groups, Proc. Amer. Math. Soc. 120 (1994), 1299-1308
10. D. DIKRANJAN AND I. PRODANOV, Totally minimal groups, Ann. Univ. Sofia Fac. Math. Méc. 69 (1974/75) 5-11
11. D. DIKRANJAN and IV. PRODANOV, A class of compact Abelian groups, Annuaire Univ. Sofia, Fac. Math. Méc. 70, (1975/76) 191-206. MR 84f:22001
12. D. DIKRANJAN, IV. PRODANOV AND L. STOYANOV, Topological Groups; Characters, Dualities and Minimal Group Topologies, Pure and Applied Mathematics, Vol. 130, Marcel Dekker Inc., New York-Basel, 1989
13. D. DIKRANJAN AND D. SHAKHMATOV, Algebraic structure of the pseudocompact groups, Memoirs Amer. Math. Soc., 133/633, April 1998, pp. viii+83
14. D. DIKRANJAN AND W. THOLEN, Categorical Structure of Closure Operators with Applications to Topology, Algebra and Discrete Mathematics, Mathematics and its Applications, vol. 346, Kluwer Academic Publishers, Dordrecht-Boston-London 1995, pp. 358.
15. D. DIKRANJAN AND M. TKAČENKO, Sequentially complete groups; dimension and minimality, submitted
16. D. DIKRANJAN AND F. J. TRIGOS-ARRIETA, Suitable sets in some topological groups, submitted
17. E.K. VAN DOUEEN, The weight of a pseudocompact homogeneous space whose cardinality has countable cofinality, Proc. Amer. Math. Soc. 80 (1980), 678-682
18. R. ENGELKING, General Topology, Helderman Verlag, Berlin 1989
19. L. FUCHS. Infinite abelian groups, Academic Press New York and London, 1973
20. D.L. GRANT, Topological groups which satisfy an open mapping theorem, Pac. J. Math. 68 (1977) 411-423
21. E. HEWITT E K. A. ROSS, Abstract Harmonic Analysis I, Grundlehren der mathematischen Wissenschaften 115, Springer, Berlin 1963
22. T. JECH, Set Theory, Academic Press, New York (1978)
23. KHAN, M. A., The existence of totally dense subgroups in LCA group, Pac. J. Math. 112 (1984), 383-390
24. M. KURANISHI, Two elements generations on semi-simple Lie groups, Kō dai Math. Sem. Rep., 1949 (1949) 9 10
25. L. S. PONTYAGIN, Continuous groups, 2nd edition, Gostehhizdat, Mosca 1954
26. IV. PRODANOV, Precompact minimal group topologies and p-adic numbers. Annuaire Univ. Sofia Fac. Math. Méc. 66 (1971/72) 249-266
27. I. PRODANOV, Minimal topologies on countable Ahelian groups, Annuaire Univ. Sofia Fac. Math. Méc. 70 (1975/76) 107-118. MR 84h:22007
28. D. SHAKHAMTOV, Character and pseudocharacter in minimal topological groups, Math. Notes 38 (1985), 1003-1006. Russian original: Mat. Zametki 38 (1985), 908-914
29. D. SHAKHAMTOV, Character and pseudocharacter in minimal topological groups, Math. Notes 38 (1985), 1003-1006. Russian original: Mat. Zametki 38 (1985), 908-914
30. R.M. STEPHENSON, Jr., Minimal topological groups, Math. Ann. 192 (1971), 193-195
31. L. STOYANOV, A property of precompact minimal abelian groups, Ann. Univ. Sofia Fac. Math. Méc. 70 (1975/76) 253-260
32. L. STOYANOV, Weak periodicity and minimality of topological groups, Annuaire Univ. Sofia Fac. Math. Méc. 73 (1978/79), 155-167
33. th Conf. of the Union of Bulg. Math., Sunny Beach 1981, 203-208
34. M.G. TKAČENKO, On countably compact and pseudocompact topologies on free Abelian groups, Soviet Math. (Izv. VUZ) 34 (5) (1990), 79-86
35. Russian original in: Izv. Vyssh. Uchebn. Zaved. Ser. Matem. 5 (1990). 68-75
36. A. TONOLO, On the classes of dense and closed subobjects, Jour. Pure Appl. Algebra 110, no. 1, (1996), 81-89
37. A. TONOLO, Total C-denseness, Comm. Algebra 24, no. 7 (1996), 2325-2339
38. N.T. VAROPOLOUS, A theorem on the continuity of homomorphism of locally compact groups, Proc. Cambridge Philos. Soc., 60 (1964) 449-463