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arXiv · 1803.09101

Every component of a fractal square is a Peano continuum

Jun Luo·Hui Rao·Ying Xiong
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Abstract

This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or more of them and form an iterated function system. The attractor F resulted from this IFS is called a fractal square. We prove that every component of F is locally connected. The same result for three-dimensional analogues of F does not hold.

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Jun Luo, Hui Rao, Ying Xiong. 2018-03-24. Every component of a fractal square is a Peano continuum. https://arxiv.org/abs/1803.09101

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