Relations between topological and metrical properties of self-affine Sierpinski sponges

作者：Zhang, Yuan; Huang, Liang-yi^*

来源：Journal of Mathematical Analysis and Applications, 2022, 514(1): 126295.

DOI：10.1016/j.jmaa.2022.126295

• Self-affine Sierpinski sponge
• delta-connected component
• Gap sequence

We investigate two Lipschitz invariants of metric spaces defined by delta-connected components, called the maximal power law property and the perfectly disconnectedness. The first property has been studied in literature for some self-similar sets and Bedford-McMullen carpets, while the second property seems to be new. For a self-affine Sierpinski sponge E, we first show that E satisfies the maximal power law if and only if E and all its major projections contain trivial connected components; secondly, we show that E is perfectly disconnected if and only if E and all its major projections are totally disconnected.

• 单位
  重庆大学