One residual set of Cantor graphs with dense conjugacy classes

2026/07/23 by Zhengyu Yin
Mathematics · #math.DS

paper · pdf

This version has been withdrawn due to a fundamental error affecting the main results

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

In this paper, we consider the space Graph(C) of all closed graphs on the Cantor set C. Equipping this space with Hausdorff metric and employing combinatorial methods, we see that the residual isomorphism classes in the space of single-valued continuous maps on the Cantor set are no longer a G_δ set but still dense in Graph(C), and we prove that the set consisting of elements with dense conjugacy classes is a dense G_δ subset of Graph(C). Finally, we prove that the set consisting of elements with zero topological entropy is a dense G_δ set in Graph(C).

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