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Extremal pseudocompact Abelian groups are compact metrizable
Author(s):
W.
W.
Comfort;
Jan
van Mill
Journal:
Proc. Amer. Math. Soc.
135
(2007),
4039-4044.
MSC (2000):
Primary 22A05, 22B05
Posted:
August 30, 2007
MathSciNet review:
2341956
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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:
-
- 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.
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- 12.
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- 13.
- E. Hewitt and K. A. Ross, Abstract harmonic analysis I, Springer-Verlag, New York-Heidelberg-Berlin, 1979. MR 551496 (81k:43001)
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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:
10.1090/S0002-9939-07-08952-6
PII:
S 0002-9939(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
Posted:
August 30, 2007
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2007,
American Mathematical Society
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