具有有限分解复杂度和渐近性质C的度量空间

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.23952/jnfa.2021.15

Jingming Zhu, WU Yan, J. Zhu, WU Y.

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引用次数: 2

摘要

对于任意k∈N，我们构造了一类度量空间Xω+k，其超有限渐近维数和互补有限渐近维数都是ω+k，其中ω是最小的无穷序数;构造了一个度量空间Y2ω，其超有限渐近维数和互补有限渐近维数都是2ω。最后，我们引入了一个称为分解维数(decodim)的几何属性。利用分解维数证明了度量空间Xω+k和Y2ω具有有限的分解复杂度。

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Metric spaces with asymptotic property C and finite decomposition complexity

We construct a class of metric spaces Xω+k whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both ω+k for any k ∈N, where ω is the smallest infinite ordinal number and a metric space Y2ω whose transfinite asymptotic dimension and complementary-finite asymptotic dimension are both 2ω . Finally, we introduce a geometric property called decomposition dimension (decodim). Using decomposition dimension, we prove that the metric spaces Xω+k and Y2ω have finite decomposition complexity.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.