On the Assouad dimension and convergence of metric spaces
Metric Geometry
2020-01-17 v3
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 a example containing all compact metric spaces as pseudo-cones, and examples containing all proper length spaces as tangent cones or asymptotic cones.
Keywords
Cite
@article{arxiv.1911.07455,
title = {On the Assouad dimension and convergence of metric spaces},
author = {Yoshito Ishiki},
journal= {arXiv preprint arXiv:1911.07455},
year = {2020}
}