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}
}