A characterization of metric subspaces of full Assouad dimension

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.

The definition of tiling spaces is modified. Schief's papers are added to Reference. This paper will appear in J. Fractal. Geom