论文标题
封闭子集的Hausdorff尺寸
Hausdorff dimension of closed subsets in profinite groups
论文作者
论文摘要
相对于给定的过滤，一个基于次数的涂鸦组可以自然地看作是一个度量空间，因此，它具有明确的Hausdorff尺寸函数。 Barnea和Shalev发现了一个理论上的理论表达方式，用于涂鸦集团$ g $的封闭子组的Hausdorff维度，以这种方式开放了一大堆探索的可能性。在本文中，我们将Barnea和Shalev的结果推广为$ G $的任意关闭子集。
A countably based profinite group can be naturally seen as a metric space with respect to a given filtration, and thus, it has a well defined Hausdorff dimension function. Barnea and Shalev found a group theoretical expression for the Hausdorff dimension of the closed subgroups of a profinite group $G$, opening, in this way, a bunch of possibilities to explore. In this paper we generalize Barnea's and Shalev's result to arbitrary closed subsets of $G$.
