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Abstract <p> Recently, Glasner, Huang, Shao, Weiss and Ye proved that the maximal infinite-step pro-nilfactor of a minimal system is a topological characteristic factor in a certain sense. In this paper, we extend their work to the product of finitely many minimal systems and determine the sharp order for a pro-nilfactor to qualify as a topological characteristic factor. As an application of our results, we characterize the complexity of most fibers within a minimal system from a topological perspective. As a corollary, we prove conjectures proposed by Huang et al. for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb Z\)</EquationSource> </InlineEquation>-actions. </p>

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Saturation of Product Systems and Applications

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Jiahao Qiu,
  • Hui Xu,
  • Xiangdong Ye,
  • Jiaqi Yu

摘要

Abstract

Recently, Glasner, Huang, Shao, Weiss and Ye proved that the maximal infinite-step pro-nilfactor of a minimal system is a topological characteristic factor in a certain sense. In this paper, we extend their work to the product of finitely many minimal systems and determine the sharp order for a pro-nilfactor to qualify as a topological characteristic factor. As an application of our results, we characterize the complexity of most fibers within a minimal system from a topological perspective. As a corollary, we prove conjectures proposed by Huang et al. for \(\mathbb Z\) -actions.