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 | References | Similar Articles | Additional Information

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.

**[1]**Eric K. van Douwen,*𝛽𝑋 and fixed-point free maps*, Topology Appl.**51**(1993), no. 2, 191–195. MR**1229715**, https://doi.org/10.1016/0166-8641(93)90152-4**[2]**Eric K. van Douwen and Jan van Mill,*The homeomorphism extension theorem for 𝛽𝜔_s𝜔*, Papers on general topology and applications (Madison, WI, 1991) Ann. New York Acad. Sci., vol. 704, New York Acad. Sci., New York, 1993, pp. 345–350. MR**1277871**, https://doi.org/10.1111/j.1749-6632.1993.tb52537.x**[3]**James Dugundji and Andrzej Granas,*Fixed point theory. I*, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR**660439****[4]**Klaas Pieter Hart and Jan van Mill,*Open problems on 𝛽𝜔*, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 97–125. MR**1078643****[5]**I. I. Parovičenko,*A universal bicompact of weight*, Soviet Math. Dokl.**4**(1963), 592-592.**[6]**J. Vermeer,*Frolík’s theorem for basically disconnected spaces*, Acta Univ. Carolin. Math. Phys.**34**(1993), no. 2, 135–142. Selected papers from the 21st Winter School on Abstract Analysis (Poděbrady, 1993). MR**1282976****[7]**-,*Fixed-point sets of continuous functions of extremally disconnected spaces*, Trans. Amer. Math. Soc. (to appear).

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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