Hausdorffen dimentsioa talde profinituetan

Abstract

The notions of Hausdorff dimension and box dimension are basic concepts in the field of fractal geometry. These concepts generalise the idea of the traditional topological dimension since, while the fractal dimension of a common geometric object coincides with the value of its typical dimension, certain pathological sets which, intuitively, do not have such a clear dimension, may have non-integer fractal dimension. In the last decades, the concept of Hausdorff dimension has provided fruitful and interesting applications in the context of countably based profinite groups, as these groups can always be seen as metric spaces. In this paper, on the one hand, we will give a general introduction to the theory of Hausdorff and box dimensions. On the other hand, we will see different significant results concerning Hausdorff dimension in profinite groups, focusing on two specific areas: the Hausdorff spectrum and R-analytic groups.