同构公制平均维度水平集的密度

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-02-10 DOI:10.1007/s10884-023-10344-5

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引用次数: 0

摘要

Abstract Let N be an n-dimensional compact riemannian manifold, with \(n\ge 2\) .在本文中，我们证明了对于任意一个（在 [0,n]\ 中的）N 上的同构，其上下度量平均维数等于（\alpha \）的集合在（\text {Hom}(N)\) 中是密集的。更一般地说，给定 \(alpha ,\beta \in [0,n]\), with \(alpha \le \beta \), 我们证明了由 N 上下层度量平均维度等于 \(alpha \)和上层度量平均维度等于 \(beta \)的同构组成的集合在 \(\text {Hom}(N)\) 中是密集的。此外，我们还证明了上度量平均维度等于 n 的同构集合在（text {Hom}(N)\) 中是残余的。

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Density of the Level Sets of the Metric Mean Dimension for Homeomorphisms

Abstract

Let N be an n-dimensional compact riemannian manifold, with \(n\ge 2\) . In this paper, we prove that for any \(\alpha \in [0,n]\) , the set consisting of homeomorphisms on N with lower and upper metric mean dimensions equal to \(\alpha \) is dense in \(\text {Hom}(N)\) . More generally, given \(\alpha ,\beta \in [0,n]\) , with \(\alpha \le \beta \) , we show the set consisting of homeomorphisms on N with lower metric mean dimension equal to \(\alpha \) and upper metric mean dimension equal to \(\beta \) is dense in \(\text {Hom}(N)\) . Furthermore, we also give a proof that the set of homeomorphisms with upper metric mean dimension equal to n is residual in \(\text {Hom}(N)\) .

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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.