论文标题
分形立方体的尺寸下降现象
A dimension drop phenomenon of fractal cubes
论文作者
论文摘要
让E为度量空间。我们介绍了E的连接性索引的概念，哪个是Hausdor？ E.非平凡连接组件的结合的维度，我们表明分形多维数据集E的连接性指数严格小于Hausdor？ E的维度规定E具有微不足道的连接组件。因此，连接索引是一个新的Lipschitz不变。此外，我们研究了连接性指数和拓扑效果的关系？方面。
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 connectedness index of a fractal cube E is strictly less than the Hausdor? dimension of E provided that E possesses a trivial connected component. Hence the connectedness index is a new Lipschitz invariant. Moreover, we investigate the relation between the connectedness index and topological Hausdor? dimension.
