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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed-point sets of autohomeomorphisms of compact $ F$-spaces


Authors: K. P. Hart and J. Vermeer
Journal: Proc. Amer. Math. Soc. 123 (1995), 311-314
MSC: Primary 54G05; Secondary 54C45, 54H25
MathSciNet review: 1260168
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Abstract: We investigate fixed-point sets of autohomeomorphisms of compact F-spaces. If the space in question is finite dimensional (in the sense of covering dimension), then the fixed-point set is a P-set; on the other hand there is an infinite-dimensional compact F-space with an involution whose fixed-point set is not a P-set.

In addition we show that under CH a closed subset of $ {\omega ^ \ast }$ is a P-set iff it is the fixed-point set of an autohomeomorphism.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1995-1260168-2
Keywords: F-space, fixed point, Čech-Stone compactification
Article copyright: © Copyright 1995 American Mathematical Society