Examples of metric spaces with asymptotic property $C$

Abstract

We construct a class of metric spaces whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $\omega +k$ for any $k\in \mathbb{N}$, where $\omega$ is the smallest infinite ordinal number and a metric space whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2\omega$. Moreover, we study the relationship between asymptotic dimension growth, transfinite asymptotic dimension and finite decomposition complexity.

arXiv admin note: text overlap with arXiv:1908.00434