Topological groups with dense compactly generated subgroups

• Fujita, Hiroshi ^[1] ; Shakhmatov, Dimitri ^[1]
  1. [1] Ehime University

     Ehime University

     Japón

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 3, Nº. 1, 2002, págs. 85-89
• Idioma: inglés
• DOI: 10.4995/agt.2002.2115
• Enlaces
  • Texto completo
• Resumen

  • A topological group G is: (i) compactly generated if it contains a compact subset algebraically generating G, (ii) -compact if G is a union of countably many compact subsets, (iii) 0-bounded if arbitrary neighborhood U of the identity element of G has countably many translates xU that cover G, and (iv) finitely generated modulo open sets if for every non-empty open subset U of G there exists a finite set F such that F  U algebraically generates G. We prove that: (1) a topological group containing a dense compactly generated subgroup is both 0-bounded and finitely generated modulo open sets, (2) an almost metrizable topological group has a dense compactly generated subgroup if and only if it is both 0-bounded and finitely generated modulo open sets, and (3) an almost metrizable topological group is compactly generated if and only if it is -compact and finitely generated modulo open sets.

• Referencias bibliográficas
  • H. Fujita and D. B. Shakhmatov, A characterization of compactly generated metrizable groups, Proc. Amer. Math. Soc., to appear.
  • I. Guran, Topological groups similar to Lindelöf groups (in Russian), Dokl. Akad. Nauk SSSR 256 (1981), no. 6, 1305-1307; English translation...
  • B.A. Pasynkov, Almost-metrizable topological groups (in Russian), Dokl. Akad. Nauk SSSR 161 (1965), 281-284.