Essential density and total density in topological groups

Journal of Group Theory

Volumn 5, Issue 3, 2002, Pages 325-350

  Comfort, W W ^a   Dikranjan, Dikran ^b  

^a WESLEYAN UNIVERSITY   (United States)

^b UNIVERSITY OF UDINE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036311596     PISSN: 14335883     EISSN: None     Source Type: Journal    
DOI: 10.1515/jgth.2002.007     Document Type: Article

References (32)

1. A. V. Arhangel'skiǐ. Cardinal invariants of topological groups. Embeddings and condensations. Dokl. Akad. Nauk SSSR 247 (1979), 779-782.
2. B. Banaschewski. Minimal topological algebras. Math. Ann. 211 (1974), 107-114.
3. E. Boschi and D. Dikranjan. Essential subgroups of topological groups. Comm. Algebra. 28 (2000), 4941-4970.
4. W. W. Comfort. Topological groups. In Handbook of set-theoretic topology (North-Holland, 1984), pp. 1143-1263.
5. W. W. Comfort and D. Dikranjan. On the poset of totally dense subgroups of compact groups. Topology Proc. 24 (1999), 103-128.
6. W. W. Comfort and D. Dikranjan. On strong totally density in topological groups. Preprint.
7. 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.
8. W. W. Comfort and S. Negrepontis. The theory of ultrafilters (Springer-Verlag, 1974).
9. W. W. Comfort and L. C. Robertson. Cardinality constraints for pseudocompact and for totally dense subgroups of compact topological groups. Pacific J. Math. 119 (1985), 265-285.
10. W. W. Comfort and K. A. Ross. Pseudocompactness and uniform continuity in topological groups. Pacific J. Math. 16 (1966), 483-496.
11. W. W. Comfort and T. Soundararajan. Pseudocompact group topologies and totally dense subgroups. Pacific J. Math. 100 (1982), 61-84.
12. S. Dierolf and U. Schwanengel. Un example d'un groupe topologique q-minimal mais non précompact. Bull. Sci. Math. (2) 101 (1977), 265-269.
13. D. Dikranjan. Zero-dimensionality of some pseudocompact groups. Proc. Amer. Math. Soc. 120 (1994), 1299-1308.
14. D. Dikranjan. Countably compact groups satisfying the open mapping theorem. Topology Appl. 98 (1999), 81-129.
15. D. Dikranjan and I. Prodanov. Totally minimal topological groups. Annuaire Univ. Sofia Fac. Math. Méc. 69 (1974/75), 5-11.
16. D. Dikranjan, I. Prodanov and L. Stoyanov. Topological groups: characters, dualities and minimal group topologies (Marcel Dekker, 1989).
17. D. N. Dikranjan and D. B. Shakhmatov. Compact-like totally dense subgroups of compact groups. Proc. Amer. Math. Soc. 114 (1992), 1119-1129.
18. E. K. van Douwen. The weight of a pseudocompact homogeneous space whose cardinality has countable cofinality. Proc. Amer. Math. Soc. 80 (1980), 678-682.
19. W. B. Easton. Powers of regular cardinals. Annals of Math. Logic 1 (1970). 139-178.
20. R. Engelking. General topology, 2nd edn. (Heldermann Verlag, 1989).
21. P. Erdös, L. Gillman, and M. Henriksen. An isomorphism theorem for real-closed fields. Ann. of Math. (2) 61 (1955), 542-554.
22. L. Gillman and M. Jerison. Rings of continuous functions (van Nostrand, 1960).
23. E. Hewitt and K. A. Ross. Abstract harmonic analysis, vol. I (Springer-Verlag, 1963).
24. K. H. Hofmann and S. A. Morris. The structure of compact groups (de Gruyter, 1998).
25. I. Prodanov. Precompact minimal group topologies and p-adic numbers, Annuaire Univ. Sofia Fac. Math. Méc. 66 (1971/72), 249-266.
26. I. Prodanov. Minimal topologies on countable Abelian groups. Annuaire Univ. Sofia Fac. Math. Méc. 70 (1975/76), 107-118.
27. I. Prodanov and L. Stoyanov. Every minimal abelian group is precompact. C. R. Acad. Bulgare Sci. 37 (1984), 23-26.
28. R. M. Stephenson, Jr. Minimal topological groups. Math. Ann. 192 (1971), 193-195.
29. L. Stoyanov. A property of precompact minimal abelian groups. Annuaire Univ. Sofia Fac. Math. Méc. 70 (1975/76), 253-260.
30. L. Stoyanov. Weak periodicity and minimality of topological groups. Annuaire Univ. Sofia Fac. Math. Méc. 73 (1978/79), 155-167.
31. L. Stoyanov. Cardinalities of minimal Abelian groups. In Proc. 10th Spring Conference Union Bulgar. Math. (Bulgarian Academy of Sciences, 1981), pp. 203-208.
32. H. Wilcox. Pseudocompact groups. Pacific J. Math. 19 (1966), 365-379.