Zig-zag chains and metric equivalences between ultrametric spaces

Abstract

We study the classification of ultrametric spaces based on their small scale geometry (uniform homeomorphism), large scale geometry (coarse equivalence) and both (all scale uniform equivalences). We prove that these equivalences can be characterized with parallel constructions using a combinatoric tool called common zig-zag chain.

16 pages

References in corpus (2)

• The coarse classification of homogeneous ultra-metric spaces
• Inverse sequences, rooted trees and their end spaces