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On fundamental groups of compact Hausdorff spaces
Author(s):
James
E.
Keesling;
Yuli
B.
Rudyak
Journal:
Proc. Amer. Math. Soc.
135
(2007),
2629-2631.
MSC (2000):
Primary 55Q05;
Secondary 03E10, 03E55, 54C30, 54D30, 54D60
Posted:
February 2, 2007
MathSciNet review:
2302585
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Abstract:
We discuss which groups can be realized as the fundamental groups of compact Hausdorff spaces. In particular, we prove that the claim ``every group can be realized as the fundamental group of a compact Hausdorff space'' is consistent with the Zermelo-Fraenkel-Choice set theory.
References:
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- 1.
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- 2.
- A. Kanamori, The Higher Infinite, Springer-Verlag, 1997. MR 1321144 (96k:03125)
- 3.
- M. Katetov, Measures in fully normal spaces. Fund. Math. 38 (1951), 73-84. MR 0048531 (14:27c)
- 4.
- J. Munkres, Topology, Second Edition, Prentice-Hall, 2000. MR 0464128 (57:4063)
- 5.
- S. Shelah, Can the fundamental (homotopy) group of a space be the rationals? Proc. Amer. Math. Soc. 103 (1988), 627-632. MR 0943095 (89g:55021)
- 6.
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Additional Information:
James
E.
Keesling
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105
Email:
jek@math.ufl.edu
Yuli
B.
Rudyak
Affiliation:
Department of Mathematics, University of Florida, 358 Little Hall, Gainesville, Florida 32611-8105
Email:
rudyak@math.ufl.edu
DOI:
10.1090/S0002-9939-07-08696-0
PII:
S 0002-9939(07)08696-0
Received by editor(s):
April 19, 2005
Received by editor(s) in revised form:
March 3, 2006
Posted:
February 2, 2007
Additional Notes:
The second author was supported by NSF grant 0406311
Communicated by:
Alexander N. Dranishnikov
Copyright of article:
Copyright
2007,
American Mathematical Society
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