Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Topologically complete groups


Author: Lawrence G. Brown
Journal: Proc. Amer. Math. Soc. 35 (1972), 593-600
MSC: Primary 22A05
MathSciNet review: 0308321
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Topologically complete groups are characterized by the existence of a compact subgroup such that the coset space is topologically complete and metrizable. Coset spaces of topologically complete groups and extensions of one topologically complete group by another are again topologically complete. The open mapping theorem is valid for topologically complete groups.


References [Enhancements On Off] (What's this?)

  • [1] Lawrence G. Brown, Note on the open mapping theorem, Pacific J. Math. 38 (1971), 25–28. MR 0308320
  • [2] -, Completeness, separability, metrizability, and extensions of topological groups (in preparation).
  • [3] E. Čech, On bicompact spaces, Ann. of Math. 39 (1937), 823-844.
  • [4] Zdeněk Frolík, Generalizations of the 𝐺_{𝛿}-property of complete metric spaces, Czechoslovak Math. J 10 (85) (1960), 359–379 (English, with Russian summary). MR 0116305
  • [5] Z. Frolík, On the topoligical product of paracompact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 8 (1960), 747–750 (English, with Russian summary). MR 0125559
  • [6] F. Hausdorff, Über innere Abbildungen, Fund. Math. 23 (1934), 279-291.
  • [7] Taqdir Husain, Introduction to topological groups, W. B. Saunders Co., Philadelphia, Pa.-London, 1966. MR 0200383
  • [8] John L. Kelley, General topology, D. Van Nostrand Company, Inc., Toronto-New York-London, 1955. MR 0070144
  • [9] E. Michael, A theorem on semi-continuous set-valued functions, Duke Math. J 26 (1959), 647–651. MR 0109343
  • [10] B. Pasynkov, Open mappings, Dokl. Akad. Nauk SSSR 175 (1967), 292–295 (Russian). MR 0217773
  • [11] B. J. Pettis, On continuity and openness of homomorphisms in topological groups, Ann. of Math. (2) 52 (1950), 293–308. MR 0038358

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22A05

Retrieve articles in all journals with MSC: 22A05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0308321-0
Keywords: Topological group, topologically complete, coset space, metrizable uniform space, open mapping
Article copyright: © Copyright 1972 American Mathematical Society