Selected Topics from the Structure Theory of Topological Groups

Open Problems in Topology II

Volumn , Issue , 2007, Pages 389-406

  Dikranjan, Dikran ^a   Shakhmatov, Dmitri ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b EHIME UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77950825980     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452208-5/50041-7     Document Type: Chapter

References (69)

1. Arhangel'skii A.V. Topological homogeneity. Topological groups and their continuous im-ages. Uspekhi Mat. Nauk 1987, 42(no. 2):69-105. (254).
2. Arhangel'skii A.V. Topological homogeneity. Topological groups and their continuous im- ages. Russian Math. Surveys 1987, 42(no. 2):83-131.
3. Banakh T., Zdomskyy L. Closed locally path-connected subspaces of finite-dimensional topological groups are locally compact 2006, Preprint.
4. Clementino M.M., Tholen W. Tychonoff's theorem in a category. Proc. Amer. Math. Soc. 1996, 124(no. 11):3311-3314.
5. W. W. Comfort, Dense subgroups of compact groups, Open problems in topology II (E. Pearl, ed.), Elsevier Science.
6. Comfort W.W., Hernández S., Remus D., Trigos-Arrieta F.J. Some open questions on topological groups. Nuclear groups and Lie groups (Madrid, 1999) 2001, 57-76. Heldermann Verlag, Lemgo.
7. Comfort W.W., Hernández S., Trigos-Arrieta F.J. Gross sections and homeomorphism classes of abelian groups equipped with the Bohr topology. Topology Appl. 2001, 115(no. 2):215-233.
8. Comfort W.W., Remus D. Imposing pseudocompact group topologies on abelian groups. Fund. Math. 1993, 142(no. 3):221-240.
9. Comfort W.W., Remus D. Abelian torsion groups with a pseudocompact group topology. Forum Math. 1994, 6(no. 3):323-337.
10. L. De Leo and D. Dikranjan, The staightening theorem for bounded codomains, Preprint.
11. Dijkstra J.J., van Mill J. Groups without convergent sequences. Topology Appl. 1996, 74:275-282.
12. Dikranjan D. Compactness and connectedness in topological groups. Topology Appl. 1998, 84:227-252.
13. Dikranjan D Continuous maps in the Bohr topology. Appl. Gen. Topol. 2001, 2(no. 2):237-270.
14. Dikranjan D. A class of abelian groups defined by continuous cross sections in the Bohr topology. Rocky Mountain J. Math. 2002, 32(no. 4):1331-1355.
15. Dikranjan D. Van Douwen's problems related to the Bohr topology. Proc. Ninth Prague Topological Symposium (1901) 2002, 37-50. Topology Atlas, Toronto.
16. Dikranjan D., Prodanov I.R., Stoyanov L.N. Topological groups: characters, dualities and minimal group topologies 1990, Marcel Dekker Inc., New York.
17. Dikranjan D., Shakhmatov D. Pseudocompact topologizations of groups. Zb. Rad. 1990, (no. 4):83-93.
18. Dikranjan D., Shakhmatov D. Pseudocompact topologies on groups. Topology Proc. 1992, 17:335-342.
19. Dikranjan D., Shakhmatov D. Algebraic structure of pseudocompact groups. Mem. Amer. Math. Soc. 1998, 133(no. 633). 83 pp.
20. Dikranjan D., Shakhmatov D. Compact-like group topologies on Abelian groups. Con- tributed problems (Zoltán Balogh Memorial Topology Conference) 2002, 6-9. http://notch.mathstat.muohio.edu/balogh/.
21. Dikranjan D., Shakhmatov D. Categorical aspects of the class of Abelian groups admit- ting a countably compact group topology 2003, Preprint.
22. Dikranjan D., Shakhmatov D. On the Markov-Zariski topology of an abelian group 2003, Preprint.
23. Dikranjan D., Shakhmatov D. Forcing hereditarily separable compact-like group topologies on abelian groups. Topology Appl. 2005, 151:2-54.
24. Dikranjan D., Shakhmatov D. Markov and Zariski topologies on the permutation group of integers 2006, Preprint.
25. Dikranjan D., Tkachenko M.G. Sequential completeness of quotient groups. Bull. Aus-tral. Math. Soc. 2000, 61(no. 1):129-150.
26. Dikranjan D., Tkachenko M.G. Varieties generated by countably compact abelian groups. Proc. Amer. Math. Soc. 2002, 130(no. 8):2487-2496.
27. Dikranjan D., Tkachenko M.G. Algebraic structure of small countably compact abelian groups. Forum Math. 2003, 15(no. 6):811-837.
28. Dikranjan D., Tkachenko M.G., Yaschenko I. On transversal group topologies. Topol-ogy Appl. 2005, 153(no. 5-6):786-817.
29. Dikranjan D., Tkachenko M.G., Yaschenko I. Transversal group topologies on non-abelian groups. Topology Appl. 2006, 153(no. 17):3338-3354.
30. Dikranjan D., Uspenskij V.V. Categorically compact topological groups. J. Pure Appl. Algebra 1998, 126:149-168.
31. Dikranjan D., Watson S. A solution to van Douwen's problem on Bohr topologies. J. Pure Appl. Algebra 2001, 163(no. 2):147-158.
32. van Douwen E.K. The product of two countably compact topological groups. Trans. Amer. Math. Soc. 1980, 262(no. 2):417-427.
33. van Douwen E.K. The maximal totally bounded group topology on G, the biggest minimal G-space, for abelian groups G. Topology Appl. 1990, 34(no. 1):69-91.
34. J. Galindo and S. García-Ferreira, Compact groups containing dense pseudocompact subgroups without non-trivial convergent sequences, Preprint.
35. J. Galindo, S. Hernández, and T. S. Wu, Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups, Op in topology II (E. Pearl, ed.), Elsevier Science.
36. Ginsburg J., Saks V. Some applications of ultrafilters in topology. Pacific J. Math. 1975, 57(no. 2):403-418.
37. Givens B.N. Closed subsets which are not retracts in the Bohr topology. Topology Appl. 2003, 129(no. 1):11-14.
38. Givens B.N., Kunen K. Chromatic numbers and Bohr topologies. Topology Appl. 2003, 131(no. 2):189-202.
39. Gladdines H. Countable closed sets that are not a retract of G#. Topology Appl. 1995, 67(no. 2):81-84.
40. Hajnal A., Juhász I. A separable normal topological group need not be Lindelo'f. General Topology and Appl. 1976, 6(no. 2):199-205.
41. Hart J.E., Kunen K. Bohr compactifications of discrete structures. Fund. Math. 1999, 160(no. 2):101-151.
42. K. Kozlov, E. Reznichenko, and O. Sipacheva, Moscow questions on topological algebra, Open problems in topology II (E. Pearl, ed.), Elsevier Science.
43. Kulesza J. Spaces which do not embed in topological groups of the same dimension. Topol-ogy Appl. 1993, 50(no. 2):139-145.
44. Kunen K. Bohr topologies and partition theorems for vector spaces. Topology Appl. 1998, 90:97-107.
45. Kunen K., Rudin W. Lacunarity and the Bohr topology. Math. Proc. Cambridge Philos. Soc. 1999, 126(no. 1):117-137.
46. Lukács G. Hereditarily h-complete groups. Topology Appl. 2004, 145:177-189.
47. Malykhin V.I. An example of a topological group. Topological spaces and their mappings 1981, 120-123. Latvijskij Gosudarstvennyj Universitet, Riga.
48. Malykhin V.I., Shapiro L.B. Pseudocompact groups without convergent sequences. Mat. Zametki 1985, 37(no. 1):103-109. Translation.
49. Malykhin V.I., Shapiro L.B. Pseudocompact groups without convergent sequences. Math. Notes 1985, 37(no. 1):59-62.
50. Markov A.A. On unconditionally closed sets. C. R. (Doklady) Acad. Sci. URSS (N.S.) 1944, 44:180-181.
51. van Mill J. Open problems in van Douwen's papers. Collected papers. 1994, Vol. I, II. North- Holland, Amsterdam.
52. Pasynkov B.A. The coincidence of various definitions of dimensionality for locally bi-compact groups. Dokl. Akad. Nauk SSSR 1960, 132:1035-1037.
53. Pasynkov B.A. The coincidence of various definitions of dimensionality for locally bi- compact groups. Soviet Math. Dokl. 1960, 1:720-722.
54. Shakhmatov D. Character and pseudocharacter in minimal topological groups. Mat. Za-metki 1985, 38(no. 6):908-914.
55. Shakhmatov D. Character and pseudocharacter in minimal topological groups. Math. Notes 1986, 39:465-470.
56. Shakhmatov D. A problem of coincidence of dimensions in topological groups. Topology Appl. 1989, 33(no. 1):105-113.
57. Shakhmatov D. Zerodimensionality of free topological groups and topological groups with noncoinciding dimensions. Bull. Polish Acad. Sci. Math. 1989, 37(no. 7-12):497-506.
58. Shakhmatov D. Imbeddings into topological groups preserving dimensions. Topology Appl. 1990, 36(no. 2):181-204.
59. Shakhmatov D. A survey of current researches and open problems in the dimension theory of topological groups. Questions Answers Gen. Topology 1990, 8(no. 1):101-128.
60. Shakhmatov D. A note on transfinite inductive dimensions in topological groups. Topology Appl. 1993, 54:213-220.
61. Sipacheva O.V. Consistent solution of Markov's problem about algebraic sets 2006, Preprint. arXiv: math. GR/0605558.
62. Sirota S.M. A product of topological groups and extremal disconnectedness. Mat. Sb. 1969, 79(121):179-192.
63. Sirota S.M. A product of topological groups, and extremal disconnectedness. Sb. Math. 1969, 8:169-180.
64. Tkachenko M.G. Gountably compact and pseudocompact topologies on free abelian groups. Izv. Vyssh. Uchebn. Zaved. Mat. 1990, (no. 5):68-75.
65. Tkachenko M.G. Gountably compact and pseudocompact topologies on free abelian groups. Soviet Math. (Iz. VUZ) 1990, 34(no. 5):79-86.
66. Tkachenko M.G. Subgroups quotient groups and products of ø-factorizable groups. Topol-ogy Proc. 1991, 16:201-231.
67. Tkachenko M.G. Provisional solution to a Comfort-van Mill problem. Topology Appl. 2002, 125(no. 1):171-182.
68. Tkachenko M.G., Yaschenko I. Independent group topologies on abelian groups. Topol-ogy Appl. 2002, 122(no. 1-2):425-451.
69. ω without non-trivial convergent sequences. Proc. Amer. Math. Soc. 2003, 131(no. 8):2617-2622.