English

A metric space with its transfinite asymptotic dimension omega + 1

Metric Geometry 2019-09-11 v2 Algebraic Topology

Abstract

We construct a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both omega+1, where omega is the smallest infinite ordinal number. Therefore, we prove that the omega conjecture is not true.

Keywords

Cite

@article{arxiv.1908.00434,
  title  = {A metric space with its transfinite asymptotic dimension omega + 1},
  author = {Yan Wu and Jingming Zhu},
  journal= {arXiv preprint arXiv:1908.00434},
  year   = {2019}
}