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Non-homeomorphic topological rank and expansiveness
Downarowicz and Maass (2008) have shown that every Cantor minimal
homeomorphism with finite topological rank is expansive. Bezuglyi,
Kwiatkowski and Medynets (2009) extended the result to non-minimal cases. On
the other hand, Gambaudo and Martens (2006) had expressed all Cantor minimal
continuou 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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