Weight of closed subsets topologically generating a compact group

Mathematische Nachrichten

Volumn 280, Issue 5-6, 2007, Pages 505-522

  Dikranjan, Dikran ^a   Shakhmatov, Dmitri ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b EHIME UNIVERSITY   (Japan)

Author keywords

Algebraic generation; Group; Topological generation; Weight

Indexed keywords

EID: 34247244776     PISSN: 0025584X     EISSN: 15222616     Source Type: Journal    
DOI: 10.1002/mana.200410499     Document Type: Article

References (25)

1. A. V. Arhangel'skil, On the relations between invariants of topological groups and their subspaces, Uspekhi Mat. Nauk 35, No. 3 (213), 3-22 (1980) (in Russian);
2. English transl. in: Russian Math. Surveys 35, No. 3, 1-23 (1980).
3. D. Dikranjan and C. Milan, Topological groups and their generators, in: Topics in Infinite Groups, edited by M. Curzio and F. De Giovanni, Quaderni di Matematica Vol. 4 (Dipartimento di Matematica, Seconda Univerità di Napoli, 2001), pp. 101-173.
4. D. Dikranjan, I. Prodanov, and L. Stoyanov, Topological Groups (Characters, Dualities and Minimal Group Topologies) (Marcel Dekker, Inc., New York-Basel, 1990).
5. D. Dikranjan and D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151, 2-54 (2005).
6. A. Dodd and R. Jensen, The core model, Ann. Math. Logic 20, 43-75 (1981).
7. A. Dodd and R. Jensen, The covering lemma for K, Ann. Math. Logic 22, 1-30 (1982).
8. A. Douady, Cohomology of totally discontinuous compact groups, Séminaire Bourbaki 5, Exp. No. 189 (Soc. Math. France, Paris, 1995), pp. 287-298.
9. E. van Douwen, The weight of a pseudocompact (homogeneous) space whose cardinality has countable cofinality, Proc. Amer. Math. Soc. 80, 678-682 (1980).
10. R. Engelking, General Topology (Helderman Verlag, Berlin, 1989).
11. E. Hewitt and K. A Ross, Abstract Harmonic Analysis I, Grundlehren der Mathematischen Wissenschaften Bd. 115 (Springer-Verlag, Berlin, 1963).
12. K.-H. Hofmann and S. A. Morris, Free compact groups III: Free semisimple compact groups, in: Proceedings of the International Conference on Categorical Topology, Prague 1988, edited by J. Adámek and S. MacLane (World Scientific, Singapore, 1989), pp. 208-219.
13. K.-H. Hofmann and S. A. Morris, Weight and c, J. Pure Appl. Algebra 68, 181-194 (1990).
14. K.-H. Hofmann and S. A. Morris, The Structure of Compact Groups. A Primer for the Studenta Handbook for the Expert, de Gruyter Studies in Mathematics Vol. 25 (Walter de Gruyter & Co., Berlin, 1998).
15. T. Jech, Set Theory: The Third Millennium Edition, revised and expanded (Springer-Verlag, Berlin, Heidelberg, 2003).
16. M. Kuranishi, Two-elements generations on semi-simple Lie groups, Kōdai Math. Sem. Rep. 1, No. 5-6, 9-10 (1949).
17. M. Magidor, On the singular cardinals problem, Part I, Israel J. Math. 28, 1-33 (1977).
18. M. Magidor, On the singular cardinals problem, Part II, Ann. of Math. (2) 106, 517-547 (1977).
19. O. Mel'nikov, Normal subgroups of free profinite groups, Izv. Akad. Nauk SSSR Ser. Mat. 42, No. 1, 3-25 (1978) (in Russian);
20. English transl, in: Math. USSR-Izv. 12, No. 1, 1-20 (1978).
21. A. Piskunov, The weight of compactly generated groups, Mat. Zametki 49, No. 4, 110-114 (1991) (in Russian);
22. English transl, in: Math. Notes 49, No, 3-4, 406-408 (1991).
23. P. Ribes and L. Zalesskii, Profinite Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete Bd. 40 (Springer-Verlag, Berlin, 2000).
24. L. Stoyanov, Weak periodicity and minimality of topological groups, Annuaire Univ. Sofia Fac. Math. Mec. 73, 155-167 (1978/79).
25. N. Varopoulos, Studies in harmonic analysis, Math. Proc. Cambridge Philos. Soc. 60, 465-516 (1964).