论文标题
自动sierpi $ \急性{\ text {n}} $ ski海绵的拓扑和度量特性之间的关系
Relations between topological and metrical properties of self-affine Sierpi$\acute{\text{n}}$ski sponges
论文作者
论文摘要
我们研究了由$Δ$连接的组件定义的两个Lipschitz的度量空间不变，称为最大功率法律属性和完美的连接。第一个物业已经在文学中研究了一些自相似集和贝德福德·麦克马伦地毯，而第二个属性似乎是新的。对于自诉Sierpi $ \急性{\ text {n}} $ Ski Sponge $ e $，我们首先显示$ e $在且仅当$ e $及其所有主要预测中都包含琐碎的连接组件时，才能满足最大功率定律；其次，我们表明$ e $完全断开了且仅当$ e $及其所有主要预测完全断开连接时。
We investigate two Lipschitz invariants of metric spaces defined by $δ$-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 Sierpi$\acute{\text{n}}$ski 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.
