Examples of metric spaces with asymptotic property $C$

Yan Wu; Jingming Zhu

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arXiv · 1912.02103

Examples of metric spaces with asymptotic property $C$

Yan Wu·Jingming Zhu

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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.

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Yan Wu, Jingming Zhu. 2019-12-03. Examples of metric spaces with asymptotic property $C$. https://arxiv.org/abs/1912.02103

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