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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Inducible periodic homeomorphisms of tree-like continua


Author: Juan A. Toledo
Journal: Trans. Amer. Math. Soc. 282 (1984), 77-108
MSC: Primary 54F20; Secondary 05C05, 54F15, 54F50, 54H15
MathSciNet review: 728704
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Abstract: In this paper we prove that every periodic homeomorphism on a tree-like continuum can be strongly induced on an inverse sequence composed of a certain kind of graph that we call ``bellows''. We introduce the concepts of ``#-graph'' of a periodic homeomorphism and of ``perfect'' homeomorphism. A theorem concerning the parallel inducing of two periodic homeomorphisms having orbit spaces with the same multiplicity structure is also proved. The results are related to conjugacy and to the pseudo-arc.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0728704-7
PII: S 0002-9947(1984)0728704-7
Keywords: Tree-like continuum, periodic homeomorphism, inducible homeomorphism, perfect homeomorphism, conjugacy, pseudo-arc
Article copyright: © Copyright 1984 American Mathematical Society