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math.MG2019★ 1 cited
A characterization of metric subspaces of full Assouad dimension
Yoshito Ishiki
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 a…
math.MG2019★ 4 cited
On the Assouad dimension and convergence of metric spaces
Yoshito Ishiki
We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric…