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- W3129129818 abstract "In this paper, we study the relationship between complementary-finite asymptotic dimension and transfinite asymptotic dimension. We prove that for every metric space X, coasdim(X)≤γ implies trasdim(X)≤γ for every countable ordinal number γ. Therefore, the metric space with complementary-finite asymptotic dimension has asymptotic property C. Furthermore, we construct an example of a metric space satisfying asymptotic property C and finite decomposition complexity with arbitrary high asymptotic dimension growth, which shows that asymptotic property C and finite decomposition complexity need not imply sub-exponential dimension growth in general." @default.
- W3129129818 created "2021-02-15" @default.
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- W3129129818 date "2021-04-01" @default.
- W3129129818 modified "2023-10-05" @default.
- W3129129818 title "The relationship between asymptotic decomposition properties" @default.
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- W3129129818 doi "https://doi.org/10.1016/j.topol.2021.107623" @default.
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