Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Fixed-point sets of autohomeomorphisms of compact $F$-spaces
HTML articles powered by AMS MathViewer

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.
References
  • Eric K. van Douwen, $\beta X$ and fixed-point free maps, Topology Appl. 51 (1993), no. 2, 191–195. MR 1229715, DOI 10.1016/0166-8641(93)90152-4
  • Eric K. van Douwen and Jan van Mill, The homeomorphism extension theorem for $\beta \omega \sbs \omega$, 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, DOI 10.1111/j.1749-6632.1993.tb52537.x
  • James Dugundji and Andrzej Granas, Fixed point theory. I, Monografie Matematyczne [Mathematical Monographs], vol. 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw, 1982. MR 660439
  • Klaas Pieter Hart and Jan van Mill, Open problems on $\beta \omega$, Open problems in topology, North-Holland, Amsterdam, 1990, pp. 97–125. MR 1078643
  • I. I. Parovičenko, A universal bicompact of weight $\aleph$, Soviet Math. Dokl. 4 (1963), 592-592.
  • 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
  • —, Fixed-point sets of continuous functions of extremally disconnected spaces, Trans. Amer. Math. Soc. (to appear).
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54G05, 54C45, 54H25
  • Retrieve articles in all journals with MSC: 54G05, 54C45, 54H25
Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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