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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Compact groups and fixed point sets


Authors: Alex Chigogidze, Karl H. Hofmann and John R. Martin
Journal: Trans. Amer. Math. Soc. 349 (1997), 4537-4554
MSC (1991): Primary 22C05, 54H25; Secondary 22D35
DOI: https://doi.org/10.1090/S0002-9947-97-02059-X
MathSciNet review: 1451595
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Abstract: Some structure theorems for compact abelian groups are derived and used to show that every closed subset of an infinite compact metrizable group is the fixed point set of an autohomeomorphism. It is also shown that any metrizable product containing a positive-dimensional compact group as a factor has the property that every closed subset is the fixed point set of an autohomeomorphism.


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Additional Information

Alex Chigogidze
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
Email: chigogid@math.usask.ca

Karl H. Hofmann
Affiliation: Fachbereich Mathematik, Technische Hochschule, Schlossgartenstrasse 7, D-64289 Darmstadt, Germany
Email: hofmann@mathematik.th-darmstadt.de

John R. Martin
Affiliation: Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada
Email: math@sask.usask.ca

DOI: https://doi.org/10.1090/S0002-9947-97-02059-X
Keywords: Compact group, character group, flow, fixed point set
Received by editor(s): December 15, 1995
Additional Notes: The first named author was partially supported by an NSERC research grant.
Article copyright: © Copyright 1997 American Mathematical Society