Abstract
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 space is bounded from below by that of any pseudo-cone of it. We exhibit an example containing all compact metric spaces as pseudo-cones, and examples containing all proper length spaces as tangent cones or asymptotic cones.
Citation
Yoshito Ishiki. "On the Assouad dimension and convergence of metric spaces." Kodai Math. J. 43 (3) 573 - 590, October 2020. https://doi.org/10.2996/kmj/1605063629
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