A characterization of compactly generated metric groups

Proceedings of the American Mathematical Society

Volumn 131, Issue 3, 2003, Pages 953-961

  Fujita, Hiroshi ^a   Shakhmatov, Dmitri ^a  

^a EHIME UNIVERSITY   (Japan)

Author keywords

Compact; Compactly generated; Convergent sequence; Metric; Metric space; Topological group

Indexed keywords

EID: 0037373935     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-02-06736-9     Document Type: Conference Paper

References (20)

1. A. V. Arhangel'skii, Linear homomorphisms of function spaces, Soviet Math. Dokl. 25 (1982), 852-855. MR 84f:54020
2. A. Arhangel'skii, O. Okunev and V. Pestov, Free topological groups over metrizable spaces, Topology Appl. 33 (1989), no. 1, 63-76. MR 90h:22002
3. W. W. Comfort and K. A. Ross, Topologies induced by groups of characters, Fund. Math. 55 (1964), 283-291. MR 30:183
4. [4] W. W. Comfort, S. A. Morris, D. Robbie, S. Svetlichny and M. Tkačenko, Suitable sets for topological groups, Topology Appl. 86 (1998), 25-46. MR 99g:54033
5. W. W. Comfort and V. Saks, Countably compact groups and finest totally bounded topologies, Pacif. J. Math. 49 (1973), 33-44. MR 51:8321
6. W. W. Comfort and F. Javier Trigos-Arrieta, Remarks on a theorem of Glicksberg, in: General Topology and Applications, Lecture Notes in Pure and Appl. Math., 134, New York (1991), 25-33. MR 92k:54042
7. I. Glicksberg, Uniform boundedness for groups, Canadian J. Math. 14 (1962), 269-276. MR 27:5856
8. M. I. Graev, Free topological groups, Izvestiya Akad. Nauk SSSR, Ser. Mat. 12 (1948), 279-324 (in Russian); English transl, in: Topology and Topological Algebra, Amer. Math. Soc. Translation Ser. 1, vol. 8 (1962), 305-364. MR 10:11d
9. K. P. Hart and J. van Mill, Discrete sets and the maximal totally bounded group topology, J. Pure Appl. Algebra 70 (1991), 73 80. MR 92c:20101
10. E. Hewitt and K. Ross, Abstract harmonic analysis, vol. I, Springer-Verlag (1963), Berlin. MR 28:158
11. Horst Leptin, Abelsche Gruppen mit kompakten Charaktergruppen und Dualitätstheorie gewisser linear topologischer abelscher Gruppen, Abh. Math. Sem. Univ. Hamburg 19 (1955), 244-263. MR 16:899f
12. A. A. Markov, On free topological groups, Doklady Akad. Nauk SSSR 31 (1941), 299-301 (in Russian)
13. [13] A. A. Markov, Three papers on topological groups, Amer. Math. Soc. Transl. 30 (1950), 120 pp. MR 12:318b
14. J. Mycielski, Some properties of connected compact groups, Colloq. Math. 5 (1958), 162-166. MR 20:6479
15. V. G. Pestov, On compactly generated topological groups, Mat. Zametki 40 (1986), 671-676 (in Russian); English transl. in: Math. Notes 40 (1986), 880-882. MR 88j:22002
16. V. Pestov, Free abelian topological groups and the Pontryagin-van Kampen duality, Bull. Austral. Math. Soc., 52, no. 2 (1995), 297-311. MR 96k:22002
17. [17] G. A. Reid, On sequential convergence in groups, Math. Zeitschrift 102 (1967), 227-235. MR 36:3069
18. [18] T. C. Stevens, Connectedness of complete metric groups, Colloq. Math. 50 (1986), 233-240. MR 88h:54056
19. A. Weil, Sur les espaces à structure uniforme et sur la Topologie Générale, Hermann, Paris (1937).
20. H. Wilcox, Dense subgroups of compact groups, Proc. Amer. Math. Soc. 28 (1971), 578-580. MR 43:6359