Fixed-point sets of autohomeomorphisms of compact 𝐹-spaces

Hart, K. P.; Vermeer, J.

doi:10.1090/S0002-9939-1995-1260168-2

Fixed-point sets of autohomeomorphisms of compact $F$-spaces
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by K. P. Hart and J. Vermeer PDF

Proc. Amer. Math. Soc. 123 (1995), 311-314 Request permission

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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