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