Categorically compact topological groups

Journal of Pure and Applied Algebra

Volumn 126, Issue 1-3, 1998, Pages 149-168

  Dikranjan, Dikran N ^a   Uspenskij, V V ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032038449     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(96)00139-9     Document Type: Article

References (40)

1. [1] A.V. Arhangel'skiǐ, Classes of topological groups, Russian Math. Surveys 36 (3) (1981) 151-174.
2. [2] S. Banach, Ueber metrische Gruppen, Studia Math. 3 (1931) 101-113.
3. [3] N. Bourbaki, General Topology, Part 1 (Addison-Wesley, Reading, MA, 1966).
4. [4] G. Castellini, Compact objects, surjectivity of epimorphisms and compactifications, Cahiers Topologie Géom. Différentielle Catégoriques, XXXI(1) (1990) 53-65.
5. [5] M.M. Clementino, Separação e compacidade em categorias, Ph.D. Thesis, Coimbra, 1992.
6. [6] M.M. Clementine and W. Tholen, Tichonov theorem for categorical compactness, Proc. Amer. Math. Soc., to appear.
7. [7] W.W. Comfort, K.-H. Hofmann and D. Remus, Topological groups and semigroups, in: M. Hušek and J. van Mill, Ed., Recent Progress in General Topology (Elsevier, Amsterdam, 1992) 315-347.
8. [8] S. Dierolf and U. Schwanengel, Un example d'un groupe topologique q-minimal mais non precompact, Bull. Sci. Math. 101 (1977) 265-269.
9. [9] S. Dierolf and U. Schwanengel, Examples of locally compact non-compact minimal topological groups, Pacific J. Math. 82 (1979) 349-355.
10. [10] D. Dikranjan and E. Giuli, Closure operators I, Topology Appl. 27 (1987) 129-143.
11. [11] D. Dikranjan and E. Giuli, Compactness, minimality and closedness with respect to a closure operator, in: S. Mac Lane and J. Adamék, Eds., Proc. Internat. Conf. on Categorical Topology, Prague, 1988 (World Scientific, Singapore, 1989) 284-296.
12. [12] D. Dikranjan and E. Giuli, Factorizations, injectivity and compactness in categories of modules, Comm. Algebra 19 (1991) 45-83.
13. [13] D. Dikranjan and I. Prodanov, Totally minimal topological groups, Ann. Univ. Sofia Fac. Math. Mec. 69 (1974/75) 5-11.
14. [14] D. Dikranjan, I. Prodanov and L. Stoyanov, Topological Groups: Characters; Dualities and Minimal Group Topologies, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 130 (Marcel Dekker, New York, 1989).
15. [15] 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, 1995).
16. [16] D. Dikranjan and A. Tonolo, On a characterization of linear compactness, Riv. Mat. Pura Appl. 16 (1995) 95-106.
17. [17] V. Eberhardt, S. Dierolf and U. Schwanengel, On products of two (totally) minimal topological groups and the three-space-problem, Math. Ann. 251 (1980) 123-128.
18. [18] R. Engelking, General Topology (Heldermann, Berlin, 2nd edn., 1989).
19. [19] T. Fay, Compact modules, Comm. Algebra 16 (1988) 1209-1219.
20. [20] T.H. Fay and G.L. Walls, A characterization of categorically compact locally nilpotent groups, Comm. Algebra 22 (1994) 3213-5225.
21. [21] I. Guran, On topological groups close to being Lindeloff, Soviet Math. Dokl. 23 (1981) 173-175.
22. [22] H. Herrlich, G. Salicrup and G. Strecker, Factorization, denseness, separation and relatively compact objects, Topology Appl. 27 (1987) 157-169.
23. [23] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol. 1 (Springer, Berlin, 2nd edn., 1979).
24. [24] K. Iwasawa, On some types of topological groups, Ann. Math. 50 (1949) 507-558.
25. [25] K. Kuratowski, Topology, Vol. 1 (Academic Press, New York, 1966).
26. [26] E.G. Manes, Compact Hausdorff objects, Gen. Topology Appl. 4 (1974) 341-360.
27. [27] S. Mrówka, Compactness and product spaces, Colloq. Math. 7 (1959) 19-22.
28. [28] A. Ol'shanskii, Geometry of defining relations in groups, in: Mathematics and its Applications (Kluwer Academic Publishers, Dordrecht, 1991).
29. [29] B.J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. Math. 52 (1950) 293-308.
30. [30] Iv. Prodanov, Some minimal group topologies are precompact, Math. Ann. 227 (1977) 117-125.
31. [31] Iv. Prodanov and L. Stoyanov, Every minimal abelian group is precompact, C.R. Acad. Bulgare Sci. 37 (1984) 23-26.
32. [32] A. Pultr and A. Tozzi, Compactness and Kuratowski theorem for locales, Cahiers Topologie Gèom. Différentielle Catégoriques 33 (1992) 3-14.
33. [33] D. Remus and L. Stoyanov, Complete minimal and totally minimal groups, Topology Appl. 42 (1991) 57-69.
34. [34] W. Roelcke and S. Dierolf, Uniform structures on topological groups and their quotients (McGraw-Hill, New York, 1981)
35. [35] S. Shelah, On a problem of Kurosh, Jonsson groups and applications, in: S.I. Adian, W. W. Boone and G. Higman, Eds., Word Problems II (North-Holland, Amsterdam, 1980) 373-394.
36. [36] R.M. Stephenson Jr., Minimal topological groups, Math. Ann. 192 (1971) 193-195.
37. [37] L. Stoyanov, Total minimality of the unitary groups, Math. Z. 187 (1984) 273-283.
38. [38] V. Uspenskij, Extensions of topological groups with a countable network, Moscow Univ. Math. Bull. 39 (5) (1984) 84-85.
39. [39] V.V. Uspenskij, Why compact groups are dyadic, in: Z. Frolik, Ed., General Topology and its Relations to Modern Analysis and Algebra VI: Proc. 6th Prague Topological Symp. 1986 (Heldermann, Berlin, 1988) 601-610.
40. [40] V. Uspenskij, On subgroups of minimal topological groups, in preparation.