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arXiv · 1911.10775

A characterization of metric subspaces of full Assouad dimension

Yoshito Ishiki
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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.

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Yoshito Ishiki. 2021-04-10. A characterization of metric subspaces of full Assouad dimension. https://arxiv.org/abs/1911.10775

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