有序度量空间的Assouad-Nagata维数和间隙

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2021-09-24 DOI:10.4171/cmh/549

A. Erschler, I. Mitrofanov

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引用次数: 4

摘要

证明了所有有限Assouad-Nagata维空间对旅行商问题都承认一个好的序，并给出了相反命题成立的充分条件。我们给出了有限维空间的一个猜想特征，从而得到了度量空间上阶效率的一个间隙陈述。在双重假设下，我们证明了给定度量空间上所有阶的一个更强的间隙现象。

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Assouad–Nagata dimension and gap for ordered metric spaces

We prove that all spaces of finite Assouad-Nagata dimension admit a good order for Travelling Salesman Problem, and provide sufficient conditions under which the converse is true. We formulate a conjectural characterisation of spaces of finite $AN$-dimension, which would yield a gap statement for the efficiency of orders on metric spaces. Under assumption of doubling, we prove a stronger gap phenomenon about all orders on a given metric space.

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来源期刊

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.