Every component of a fractal square is a Peano continuum

DOI10.1016/j.topol.2022.108271OpenAlexW4323283509MaRDI QIDQ2104993

Ying Xiong, Jun Luo, Hui Rao

Publication date: 8 December 2022

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09101

zbMATH Keywords

locally connectedPeano continuumfractal square

Mathematics Subject Classification ID

Continua and generalizations (54F15) Fractals (28A80) Connected and locally connected spaces (general aspects) (54D05)

Cites Work

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• Connectedness of a class of planar self-affine tiles
• Disk-like tiles derived from complex bases
• Self-similar sets with initial cubic patterns
• Boundary local connectivity of tiles in \(\mathbb R^2\)
• Self-affine manifolds
• On a theorem of Bandt and Wang and its extension to \(p2\)-tiles
• On the fundamental group of the Sierpiński-gasket
• Rauzy fractals with countable fundamental group
• Arcwise connectedness of the boundary of connected self-similar sets
• On the fundamental group of self-affine plane tiles
• A survey on topological properties of tiles related to number systems
• A GLUING LEMMA FOR ITERATED FUNCTION SYSTEMS
• Topological structure of fractal squares
• Fundamental groups of one-dimensional spaces
• On the structure of self-similar sets
• Separation Properties for Self-Similar Sets
• Topological properties of a class of self-affine tiles in $\mathbb {R}^3$
• Topological Properties of a Class of Higher-dimensional Self-affine Tiles
• CONNECTIVITY PROPERTIES OF SIERPIŃSKI RELATIVES
• A TECHNIQUE IN THE TOPOLOGY OF CONNECTED SELF-SIMILAR TILES
• TOPOLOGICAL STRUCTURE OF SELF-SIMILAR SETS

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