1 citations · 1 across the 2 of their papers we have counts for
5 papers
A dimension drop phenomenon of fractal cubes
Liangyi Huang, Hui Rao
Let E be a metric space. We introduce a notion of connectedness index of E, which is the Hausdor? dimension of the union of non-trivial connected components of E. We show that the…
Characterization of complementing pairs of
Hui Rao, Ya-min Yang, Yuan Zhang
Let be subsets of an abelian group . A pair is called a -pair if and is the direct sum of and . The -pairs are ch…
Space-filling curves of self-similar sets (III): Skeletons
Hui Rao, Shu-Qin Zhang
Skeleton is a new notion designed for constructing space-filling curves of self-similar sets. It is shown in [Dai, Rao and Zhang, Space-filling curves of self-similar sets (II): Ed…
Every component of a fractal square is a Peano continuum
Jun Luo, Hui Rao, Ying Xiong
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…
Lipschitz Equivalence of Self-Similar Sets: Algebraic and Geometric Properties
Hui Rao, Huo-Jun Ruan, Yang Wang
In this paper we provide an up-to-date survey on the study of Lipschitz equivalence of self-similar sets. Lipschitz equivalence is an important property in fractal geometry because…