Topological rank does not increase by natural extension of Cantor minimals

2016/07/03 by Takashi Shimomura, Shimomura, Takashi
Computer Science · Mathematics · #37B05 #37B10 #54H20 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1607.00601

openalex publication_date 2016/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Downarowicz and Maass (2008) have defined the topological rank for all Cantor minimal homeomorphisms. On the other hand, Gambaudo and Martens (2006) have expressed all Cantor minimal continuous surjections as the inverse limits of certain graph coverings. Using the aforementioned results, we previously extended the notion of topological rank to all Cantor minimal continuous surjections. In this paper, we show that taking natural extensions of Cantor minimal continuous surjections does not increase their topological ranks. Further, we apply the result to the minimal symbolic case.

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