Every component of a fractal square is a Peano continuum
General Topology
2018-03-28 v1
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.
Keywords
Cite
@article{arxiv.1803.09101,
title = {Every component of a fractal square is a Peano continuum},
author = {Jun Luo and Hui Rao and Ying Xiong},
journal= {arXiv preprint arXiv:1803.09101},
year = {2018}
}
Comments
19 pages, 10 figures