Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 60, Number 4 (2008), 1171-1185.
An absorption theorem for minimal AF equivalence relations on Cantor sets
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 -systems for [GMPS3], in a similar way as the result in [GMPS2] was needed (and sufficient) for the study of minimal -systems [GMPS1].
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 1171-1185.
First available in Project Euclid: 5 November 2008
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MATUI, Hiroki. An absorption theorem for minimal AF equivalence relations on Cantor sets. J. Math. Soc. Japan 60 (2008), no. 4, 1171--1185. doi:10.2969/jmsj/06041171. https://projecteuclid.org/euclid.jmsj/1225894037