A characterization of metric subspaces of full Assouad dimension
Yoshito Ishiki
RIKEN Center for Advanced Photonics, Wako, Japan; RIKEN Center for Advanced Photonics, Wako, Japan
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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.
Cite this article
Yoshito Ishiki, A characterization of metric subspaces of full Assouad dimension. J. Fractal Geom. 8 (2021), no. 4, pp. 363–388
DOI 10.4171/JFG/109