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arXiv · 1404.6619

On the classification of fractal squares

Jun Jason Luo·Jing-Cheng Liu
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Abstract

In \cite{LaLuRa13}, the authors completely classified the topological structure of so called {\it fractal square} $F$ defined by $F=(F+{\mathcal D})/n$, where ${\mathcal{D}}\subsetneq\{0,1,\dots,n-1\}^2, n\ge 2$. 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.

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Jun Jason Luo, Jing-Cheng Liu. 2015-08-18. On the classification of fractal squares. https://arxiv.org/abs/1404.6619

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