2020/04/29 by Iker de las Heras, Heras, Iker de las
Mathematics · Computer Science · #Advanced Topology and Set Theory #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2004.14210
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.