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October 2020 On the Assouad dimension and convergence of metric spaces
Yoshito Ishiki
Kodai Math. J. 43(3): 573-590 (October 2020). DOI: 10.2996/kmj/1605063629

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.

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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

Information

Published: October 2020
First available in Project Euclid: 11 November 2020

MathSciNet: MR4173165
Digital Object Identifier: 10.2996/kmj/1605063629

Rights: Copyright © 2020 Tokyo Institute of Technology, Department of Mathematics

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Vol.43 • No. 3 • October 2020
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