2019/11/18 by Ishiki, Yoshito
#FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1911.07455
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.