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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Continuous functions on extremally disconnected spaces


Author: J. Vermeer
Journal: Trans. Amer. Math. Soc. 347 (1995), 3263-3285
MSC: Primary 54G05; Secondary 54C15, 54H25
DOI: https://doi.org/10.1090/S0002-9947-1995-1311920-0
MathSciNet review: 1311920
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Abstract: Using results and techniques due to Abramovich, Arenson and Kitover it is shown that each fixed-point set of a selfmap of a compact extremally disconnected space is a retract of that space, and that the retraction can be constructed from the particular selfmap itself. Also, the closure of the set of periodic points turns out to be a retract of the space. Several decomposition theorems for arbitrary selfmaps on extremally disconnected spaces are obtained similar to the theorem of Frolík on embeddings. Conditions are obtained under which the set of fixed points is clopen.


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DOI: https://doi.org/10.1090/S0002-9947-1995-1311920-0
Keywords: Extremally disconnected, retracts, fixed points
Article copyright: © Copyright 1995 American Mathematical Society