局部富紧集
Locally rich compact sets
摘要：
我们构造一个紧度量空间，它在所有点上都有其他紧度量空间作为关于Gromov-Hausdorff距离的切线。此外，我们给出了欧氏单位立方体中的紧集的例子，这些紧集几乎在所有点或仅在稠密子集中具有立方体的任何其他紧集作为切线。这里的“几乎所有紧集”意味着切线集合包含立方体的任何紧集的压缩像，并且压缩比是一致有界的。在欧几里得空间中，子集之间的距离用Hausdorff距离来度量。还研究了这类空间和集合的几何性质和维数。
英文摘要：
We construct a compact metric space that has any other compact metric space as a tangent, with respect to the Gromov-Hausdorff distance, at all points. Furthermore, we give examples of compact sets in the Euclidean unit cube, that have almost any other compact set of the cube as a tangent at all points or just in a dense sub-set. Here the "almost all compact sets" means that the tangent collection contains a contracted image of any compact set of the cube and that the contraction ratios are uniformly bounded. In the Euclidean space, the distance of sub-sets is measured by the Hausdorff distance. Also the geometric properties and dimensions of such spaces and sets are studied.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
