Arcwise connectedness of the boundaries of connected self-similar sets

2003/02/24 by Tai-Man Tang, Tai‐Man Tang, Tang, Tai-Man
Mathematics · Physics and Astronomy · #28A80 (Primary) #54F65 (Secondary) #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #General Topology (math.GN) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.CA #math.GN #msc:28A80 #msc:54F65

paper · pdf · doi:10.48550/arxiv.math/0302279

6 pages, no figure

arxiv created 2003/02/24 · openalex publication_date 2003/02/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let T be the attractor of injective contractions f₁,...,f_m on R² that satisfy the Open Set Condition. If T is connected, ∂ T is arcwise connected. In particular, the boundary of the Levy dragon is arcwise connected.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

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