NON-HOMEOMORPHIC TOPOLOGICAL RANK AND EXPANSIVENESS

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Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank K>1 is expansive. Bezuglyi et al (2009) extended the result to non-minimal cases. On the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal continuous surjections as the inverse limit of graph coverings. In this paper, we define a topological rank for every Cantor minimal continuous surjection, and show that every Cantor minimal continuous surjection of finite topological rank has the natural extension that is expansive.

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