Some topological groups with and some without suitable sets

Topology and its Applications

Volumn 98, Issue 1-3, 1999, Pages 131-148

  Dikranjan, D ^a   Tkacenko M ^b   Tkachuk, V ^b  

^a UNIVERSITY OF UDINE   (Italy)

^b UNIVERSIDAD AUTÓNOMA METROPOLITANA   (Mexico)

Author keywords

Countably compact; Free topological group; Lindel f; Pseudocompact; Separable; Space of continuous functions; Strictly discrete; Suitable set; Topology of pointwise convergence; bounded

Indexed keywords

EID: 0006134507     PISSN: 0016660X     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0166-8641(98)00109-6     Document Type: Article

References (21)

1. A.V. Arhangel'skiǐ, Topological Function Spaces, Mathematics and Its Applications 78, Kluwer Academic Publishers, Dordrecht, 1992.
2. A.V. Arhangel'skiǐ, Relations between cardinal invariants of topological groups and their subspaces, Russian Math. Surveys 35 (1980) 1-23.
3. A.V. Arhangel'skiǐ, Classes of topological groups, Russian Math. Surveys 36 (1981) 151-174.
4. W.W. Comfort, S.A. Morris, D. Robbie, S. Svetlichny and M. Tkačenko, Suitable sets for topological groups, Topology Appl. 86 (1) (1998) 25-46.
5. W.W. Comfort and K.A. Ross, Pseudocompactness and uniform continuity in topological groups, Pacific J. Math. 16 (1966) 483-496.
6. W.W. Comfort and T. Soundararajan, Pseudocompact group topologies and totally dense subgroups, Pacific J. Math. 100 (1982) 61-84.
7. E.K. van Douwen, The weight of a pseudocompact homogeneous space whose cardinality has countable cofinality, Proc. Amer. Math. Soc. 80 (1980) 678-682.
8. F.R. Drake, Set Theory, North-Holland, Amsterdam, 1974.
9. D. Dikranjan, M.G. Tkačenko and V.V. Tkachuk, Topological groups with thin generating sets, J. Pure Appl. Algebra, to appear.
10. J. Ginsburg and V. Saks, Some applications of ultrafilters in topology, Pacific J. Math. 57 (1975) 403-418.
11. G. Gruenhage, Generalized metric spaces, in: K. Kunen and J. Vaughan, eds., Handbook of Set-Theoretic Topology, Elsevier, Amsterdam, 1984, pp. 423-501.
12. K.-H. Hofmann and S.A. Morris, Weight and c, J. Pure Appl. Algebra 68 (1990) 181-194.
13. A.V. Ivanov, On bicompacta all finite powers of which are hereditarily separable, Soviet Math. Dokl. 19 (1978) 1470-1473.
14. I. Juhász, On closed discrete subspaces of product spaces, Bull. Acad. Polon. Sci. Ser. Math. 17 (1969) 219-223.
15. K. Kunen, Set Theory. An Introduction to Independence Proofs, Studies in Logic 102, North-Holland, Amsterdam, 1980.
16. S. Mrówka, On E-compact spaces, Bull. Acad. Polon. Sci. Série Math., Astr. Phys. 14 (1966) 597-605.
17. E.C. Nummela, Uniform free topological groups and Samuel compactifications, Topology Appl. 13 (1982) 77-83.
18. O.G. Okunev and K. Tamano, Lindelöf powers and products of function spaces, Proc. Amer. Math. Soc. 124 (1996) 2905-2916.
19. V.G. Pestov, Some properties of free topological groups, Moscow Math. Bull. 37 (1982) 46-49.
20. M.G. Tkačenko, Examples of connected left-separated spaces and topological groups, Acta Math. Acad. Sci. Hungar. 38 (1981) 257-261.
21. F.J. Trigos-Arrieta and A. Tomita, Suitable sets in products of topological groups and in groups equipped with the Bohr topology, in: D. Dikranjan and L. Salce, eds., Abelian Groups, Module Theory and Topology: Proceedings in Honour of Adalberto Orsatti's 60-th birthday, Lecture Notes in Pure Appl. Math. 201, Marcel Dekker, New York, 1998.