Fixed-point sets of autohomeomorphisms of compact -spaces

Authors:
K. P. Hart and J. Vermeer

Journal:
Proc. Amer. Math. Soc. **123** (1995), 311-314

MSC:
Primary 54G05; Secondary 54C45, 54H25

DOI:
https://doi.org/10.1090/S0002-9939-1995-1260168-2

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 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