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)

 
 

 

Extremal pseudocompact Abelian groups are compact metrizable


Authors: W. W. Comfort and Jan van Mill
Journal: Proc. Amer. Math. Soc. 135 (2007), 4039-4044
MSC (2000): Primary 22A05, 22B05
DOI: https://doi.org/10.1090/S0002-9939-07-08952-6
Published electronically: August 30, 2007
MathSciNet review: 2341956
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Every pseudocompact Abelian group of uncountable weight has both a proper dense pseudocompact subgroup and a strictly finer pseudocompact group topology.


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

  • 1. W. W. Comfort and J. Galindo, Extremal pseudocompact topological groups, J. Pure Appl. Algebra 197 (2005), 59-81. MR 2123980 (2006a:22001)
  • 2. W. W. Comfort, H. Gladdines, and J. van Mill, Proper pseudocompact subgroups of pseudocompact abelian groups, Annals of the New York Ac. Sci. 728 (1994), 237-247. MR 1467777 (99g:22005)
  • 3. W. W. Comfort and J. van Mill, Concerning connected, pseudocompact Abelian groups, Top. Appl. 33 (1989), 21-45. MR 1020981 (90k:54002)
  • 4. W. W. Comfort and J. van Mill, Extremal pseudocompact Abelian groups are compact metric, Abstracts Amer. Math. Soc. 27 (2006), p. 78 (Abstract #1014-22-958).
  • 5. W. W. Comfort and J. van Mill, Extremal pseudocompact abelian groups: A brief exposé, in preparation.
  • 6. W. W. Comfort and L. C. Robertson, Proper pseudocompact extensions of compact abelian group topologies, Proc. Amer. Math. Soc. 86 (1982), 173-178. MR 663891 (83k:22011)
  • 7. W. W. Comfort and Lewis C. Robertson, Extremal phenomena in certain classes of totally bounded groups, Dissertationes Math. (Rozprawy Mat.) 272 (1988), 1-42. MR 959432 (89i:22001)
  • 8. W. W. Comfort and K. A. Ross, Pseudocompactness and uniform continuity in topological groups, Pac. J. Math. 16 (1966), 483-496. MR 0207886 (34:7699)
  • 9. W. W. Comfort and T. Soundararajan, Pseudocompact group topologies and totally dense subgroups, Pacific J. Math. 100 (1982), 61-84. MR 661441 (83m:22008)
  • 10. D. Dikranjan, G. Bruno, and C. Milan, Weakly metrizable pseudocompact groups, to appear in Appl. Gen. Top.
  • 11. L. Fuchs, Infinite abelian groups. Vol. I, Academic Press, New York, 1970. MR 0255673 (41:333)
  • 12. J. Galindo, Dense pseudocompact subgroups and finer pseudocompact group topologies, Sci. Math. Jpn. 55 (2002), 627-640. MR 1901051 (2003b:54041)
  • 13. E. Hewitt and K. A. Ross, Abstract harmonic analysis I, Springer-Verlag, New York-Heidelberg-Berlin, 1979. MR 551496 (81k:43001)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 22A05, 22B05

Retrieve articles in all journals with MSC (2000): 22A05, 22B05


Additional Information

W. W. Comfort
Affiliation: Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459
Email: wcomfort@wesleyan.edu

Jan van Mill
Affiliation: Faculteit Exacte Wetenschappen, Afdeling Wiskunde, Vrije Universiteit, De Boelelaan 1081A, 1081 HV Amsterdam, The Netherlands
Email: vanmill@cs.vu.nl

DOI: https://doi.org/10.1090/S0002-9939-07-08952-6
Keywords: Pseudocompact topological group, extremal topological group, proper dense pseudocompact subgroup, Abelian
Received by editor(s): November 20, 2005
Received by editor(s) in revised form: September 2, 2006
Published electronically: August 30, 2007
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2007 American Mathematical Society

American Mathematical Society