Sequential completeness of quotient groups

Bulletin of the Australian Mathematical Society

Volumn 61, Issue 1, 2000, Pages 129-150

  Dikranjan, Dikran ^a   Tkačenko, Michael ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b DEPARTAMENTO DE QUÍMICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034134624     PISSN: 00049727     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0004972700022085     Document Type: Article

References (49)

1. A.V. Arhangel'skiǐ, 'Cardinal invariants of topological groups. Embeddings and condensations', Soviet Math. Dokl. 20 (1979), 783-787. Russian original in: Dokl. AN SSSR 247 (1979), 779-782.
2. A.V. Arhangel'skiǐ, 'Cardinal invariants of topological groups. Embeddings and condensations', Soviet Math. Dokl. 20 (1979), 783-787. Russian original in: Dokl. AN SSSR 247 (1979), 779-782.
3. A.V. Arhangel'skiǐ, 'Classes of topological groups', Russian Math. Surveys 36 (1981), 151-174. Russian original in: Uspekhy Mat. Nauk 36 (1981), 127-146.
4. A.V. Arhangel'skiǐ, 'Classes of topological groups', Russian Math. Surveys 36 (1981), 151-174. Russian original in: Uspekhy Mat. Nauk 36 (1981), 127-146.
5. A.V. Arhangel'skiǐ, 'Spaces of functions with the pointwise convergence topology and compacta', (in Russian), Uspekhy Mat. Nauk 39 (1984), 11-50.
6. A.V. Arhangel'skiǐ and V.I. Ponomarev, 'On dyadic compacta', (in Russian), Dokl. Akad. Nauk SSSR 182 (1968), 993-996.
7. W.W. Comfort, 'Problems on topological groups and other homogeneous spaces', in Open problems in topology, (J. van Mill and G. M. Reed, Editors) (North-Holland, Amsterdam 1990), pp. 313-347.
8. W.W. Comfort and J. van Mill, 'On the existence of free topological groups' Topology Appl. 29 (1988), 245-269.
9. W.W. Comfort, S.A. Morris, D. Robbie, S. Svetlichny and M.G. Tkačenko, 'Suitable sets for topological groups', Topology Appl. 86 (1998), 25-46.
10. W.W. Comfort and L. Robertson, 'Extremal phenomena in certain classes of totally bounded groups', Dissert. Math. 272 (1988), 1-48.
11. W.W. Comfort and K. Ross, 'Pseudocompactness and uniform continuity in topological groups', Pacific J. Math. 16 (1966), 483-496.
12. W.W. Comfort and V. Saks, 'Countably compact groups and the finest totally bounded topologies', Pacific J. Math. 49 (1973), 33-44.
13. W.W. Comfort and F.J. Trigos-Arrieta, 'Remarks on a theorem of Glicksberg', in General topology and its applications, (S.J. Andima, R. Kopperman, P.R. Misra, J.Z. Reichman and A.R. Todd, Editors), Lecture Notes in Pure and Applied Mathematics 134 (Marcel Dekker, New York, 1991), pp. 25-33.
14. H.H. Corson, 'Normality of subsets of product spaces', Amer. J. Math. 81 (1959) 785-796.
15. D. Dikranjan, 'Zero-dimensionality of some pseudocompact groups', Proc. Amer. Math. Soc. 120 (1994), 1299-1308.
16. D. Dikranjan, 'Countably compact groups satisfying the open mapping theorem', Topology Appl. (to appear).
17. D. Dikranjan, Iv. Prodanov and L. Stoyanov, Topological groups: Characters, dualities and minimal group topologies, Pure and Applied Mathematics 130 (Marcel Dekker Inc., New York, Basel, 1989).
18. D. Dikranjan and W. Tholen, Categorical structure of closure operators with applications to topology, Algebra and discrete mathematics, Mathematics and its Applications 346 (Kluwer Academic Publishers, Dordrecht, Boston, London, 1995).
19. D. Dikranjan and M. Tkačenko, 'Sequentially complete groups: dimension and minimality', J. Pure. Appl. Algebra (to appear).
20. D. Dikranjan and M. Tkačenko, 'Weak completeness of free topological groups', Topology Appl. (to appear).
21. D. Dikranjan and A. Tonolo, 'On a characterization of linear compactness', Riv. Mat. Pura Appl. 17 (1995), 95-106.
22. D. Dikranjan and V. Uspenskiǐ, 'Categorically compact topological groups', J. Pure Appl. Algebra 85 (1998), 53-91.
23. E. K. van Douwen, 'The product of two countably compact topological groups', Trans. Amer. Math. Soc. 262 (1980), 417-427.
24. 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.
25. P. Flor, 'Zur Bohr-Konvergenz von Folgen', Math. Scand. 23 (1968), 169-170.
26. ω-spaces', Topology Proc. 2 (1977), 111-124.
27. I. Glicksberg, 'Uniform boundedness for groups', Canad. J. Math. 14 (1962), 269-276.
28. M.I. Graev, 'Free topological groups', Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-323. English translation in: Topology and Topological Algebra, Translation Series 1, 8 American Mathematical Society (1962), pp. 305-364.
29. M.I. Graev, 'Free topological groups', Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 279-323. English translation in: Topology and Topological Algebra, Translation Series 1, 8 American Mathematical Society (1962), pp. 305-364.
30. D.L. Grant, 'Topological groups which satisfy an open mapping theorem', Pacific J. Math. 68 (1977), 411-423.
31. S.P. Gul'ko, 'On properties of subsets of Σ-products', (in Russian), Dokl. Akad. Nauk SSSR 237 (1977).
32. I. Guran, 'On topological groups close to being Lindelöf, Soviet Math. Dokl. 23 (1981), 173-175.
33. K.-H. Hofmann and S.A. Morris, 'Weight and c', J. Pure Appl. Algebra 68 (1990), 181-194.
34. D.C. Hunt and S.A. Morris, 'Free subgroups of free topological groups', in Proc. Second Internat. Conf. on the Theory of Groups, Canberra, 1973, Lecture Notes in Mathematics 372 (Springer-Verlag, Berlin, Heidelberg, New York, 1974), pp. 377-387.
35. J. Mack, S.A. Morris and E.T. Ordman, 'Free topological groups and the projective dimension of locally compact Abelian group', Proc. Amer. Math. Soc. 40 (1973), 303-308.
36. S.A. Morris, 'Varieties of topological groups: a survey', Colloq. Math. 46 (1982), 147-165.
37. N. Noble, 'The continuity of functions on Cartesian products', Trans. Amer. Math. Soc. 149 (1970), 187-198.
38. E.C. Nummela, 'Uniform free topological groups and Samuel compactifications', Topology Appl. 13 (1982), 77-83.
39. V.G. Pestov, 'Some properties of free topological groups', Moscow Univ. Math. Bull. 37 (1982), 46-49.
40. Iv. Prodanov, 'Some minimal group topologies are precompact', Math. Ann. 227 (1977), 117-125.
41. I.V. Protasov, 'Minimal varieties of topological groups', (in Russian), Dokl. Akad. Nauk Ukrain. SSR Ser. A 8 (1988), 14-16.
42. D.A. Raǐkov, 'A criterion of completeness of topological linear spaces and topological Abelian groups', (in Russian), Mat. Zametky 16 (1974), 101-106.
43. D. Remus and L. Stoyanov, 'Complete minimal and totally minimal groups', Topology Appl. 42 (1991), 57-69.
44. D.J.F. Robinson, A course in the theory of groups (Springer-Verlag, Berlin, Heidelberg, New York, 1982).
45. M.G. Tkačenko, 'Compactness type properties in topological groups', Czech. Math. J. 38 (1988), 324-341.
46. M.G. Tkačenko, 'Strong collectionwise normality and countable compactness in free topological groups', Siberian Math. J. 28 (1987), 167-177.
47. M.G. Tkačenko, 'Pseudocompact topological groups and their properties', Siberian Math. J. 30 (1989), 154-164.
48. M.G. Tkačenko, 'Countably compact and pseudocompact topologies on free Abelian groups', Soviet Math. (Iz. VUZ) 34 (1990), 79-86.
49. J. Vaughan, 'Countably compact and sequentially compact spaces', in Handbook of set-theoretic topology, (K. Kunen and J.E. Vaughan, Editors) (North-Holland, Amsterdam, New York, Oxford, 1984), pp. 569-602.