Compact groups and fixed point sets

Chigogidze, Alex; Hofmann, Karl; Martin, John

doi:10.1090/S0002-9947-97-02059-X

Compact groups and fixed point sets
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by Alex Chigogidze, Karl H. Hofmann and John R. Martin PDF

Trans. Amer. Math. Soc. 349 (1997), 4537-4554 Request permission

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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