论文标题
无限的恒定间隙长度树木中的厚综合产品
Infinite constant gap length trees in products of thick Cantor sets
论文作者
论文摘要
我们表明，足够厚的Cantor套件的产品在平面上产生树木，在相邻顶点之间持续距离。此外，我们证明了此距离的一组选择具有非空的内饰。我们允许我们的树木是无限的，这进一步将这项工作与分形集中的模式的先前结果区分开来。这建立在作者以前的图形和距离距离距离纽豪斯厚度的产品的距离集的基础上。
We show that products of sufficiently thick Cantor sets generate trees in the plane with constant distance between adjacent vertices. Moreover, we prove that the set of choices for this distance has non-empty interior. We allow our trees to be countably infinite, which further distinguishes this work from previous results on patterns in fractal sets. This builds on the authors' previous work on graphs and distance sets of products of Cantor sets of sufficient Newhouse thickness.
