English

Zig-zag chains and metric equivalences between ultrametric spaces

Geometric Topology 2009-09-02 v1 Combinatorics

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.

Keywords

Cite

@article{arxiv.0909.0153,
  title  = {Zig-zag chains and metric equivalences between ultrametric spaces},
  author = {Álvaro Martínez-Pérez},
  journal= {arXiv preprint arXiv:0909.0153},
  year   = {2009}
}

Comments

16 pages

R2 v1 2026-06-21T13:41:06.338Z