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October, 2008 An absorption theorem for minimal AF equivalence relations on Cantor sets
Hiroki MATUI
J. Math. Soc. Japan 60(4): 1171-1185 (October, 2008). DOI: 10.2969/jmsj/06041171


We prove that a ‘small’ extension of a minimal AF equivalence relation on a Cantor set is orbit equivalent to the AF relation. By a ‘small’ extension we mean an equivalence relation generated by the minimal AF equivalence relation and another AF equivalence relation which is defined on a closed thin subset. The result we obtain is a generalization of the main theorem in [GMPS2]. It is needed for the study of orbit equivalence of minimal Z d -systems for d>2 [GMPS3], in a similar way as the result in [GMPS2] was needed (and sufficient) for the study of minimal Z 2 -systems [GMPS1].


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Hiroki MATUI. "An absorption theorem for minimal AF equivalence relations on Cantor sets." J. Math. Soc. Japan 60 (4) 1171 - 1185, October, 2008.


Published: October, 2008
First available in Project Euclid: 5 November 2008

zbMATH: 1170.37009
MathSciNet: MR2467874
Digital Object Identifier: 10.2969/jmsj/06041171

Primary: ‎37B05‎

Keywords: Cantor sets , minimal dynamical systems , orbit equivalence

Rights: Copyright © 2008 Mathematical Society of Japan


Vol.60 • No. 4 • October, 2008
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