On the classification of fractal squares

2014/04/26 by Jun Luo, Jun Jason Luo, Luo, Jun Jason +3 · 1 citation
Computer Science · Mathematics · #05C63 #54F65 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Primary 28A80 #Secondary 53C23 #Topological and Geometric Data Analysis #math.GN #math.MG #msc:05C63 #msc:28A80 #msc:53C23 #msc:54F65

paper · pdf · doi:10.48550/arxiv.1404.6619

16 pages, 12 figures

openalex publication_date 2014/04/26 · arxiv created 2015/08/18 · arxiv updated 2015/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeLaLuRa13, the authors completely classified the topological structure of so called \it fractal square F defined by F=(F+\mathcal D)/n, where D\subsetneq\0,1,…,n-1\², n≥ 2. In this paper, we further provide simple criteria for the F to be totally disconnected, then we discuss the Lipschitz classification of F in the case n=3, which is an attempt to consider non-totally disconnected sets.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

Cited by

• A Survey on the Topology of Fractal Squares

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