Jingming Zhu, Yan Wu, Metric spaces with asymptotic property C and finite decomposition complexity, Vol. 2021 (2021), Article ID 15, pp. 1-12

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DOI: 10.23952/jnfa.2021.15

Received April 13, 2021; Accepted May 7, 2021; Published May 21, 2021

Abstract. We construct a class of metric spaces $X_{\omega+k}$ 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 $Y_{2\omega}$ whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both $2\omega$ . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces $X_{\omega+k}$ and $Y_{2\omega}$ have finite decomposition complexity.

How to Cite this Article:
Jingming Zhu, Yan Wu, Metric spaces with asymptotic property C and finite decomposition complexity, Journal of Nonlinear Functional Analysis, Vol. 2021 (2021), Article ID 15, pp. 1-12.