A characterization of metric subspaces of full Assouad dimension
Metric Geometry
2021-04-13 v2
Abstract
We introduce the notion of tiling spaces for metric spaces. The class of tiling spaces contains the Euclidean spaces, the middle-third Cantor set, and various self-similar spaces appearing in fractal geometry. For doubling tiling spaces, we characterize metric subspaces whose Assouad dimension coincides with that of the whole space.
Cite
@article{arxiv.1911.10775,
title = {A characterization of metric subspaces of full Assouad dimension},
author = {Yoshito Ishiki},
journal= {arXiv preprint arXiv:1911.10775},
year = {2021}
}
Comments
The definition of tiling spaces is modified. Schief's papers are added to Reference. This paper will appear in J. Fractal. Geom