Rd中的模型间集是模型集

IF 0.5 4区数学 Q3 MATHEMATICS

Indagationes Mathematicae-New Series Pub Date : 2024-09-01 DOI:10.1016/j.indag.2023.06.007

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引用次数: 0

摘要

我们证明，给定切分方案中有限多个移位模型集的任何联合都是某个修正切分方案中的模型集。限于直接空间 Rd，我们证明任何模型间集合都是某个具有第二可数内部空间的修正切分方案中的模型集合。在这两种情况下，修正的切分-投影方案中的窗口都继承了原始窗口的拓扑和度量理论性质。

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Inter-model sets in Rd are model sets

We show that any union of finitely many shifted model sets from a given cut-and-project scheme is a model set in some modified cut-and-project scheme. Restricting to direct space $R^{d}$ , we show that any inter-model set is a model set in some modified cut-and-project scheme with second countable internal space. In both cases, the window in the modified cut-and-project scheme inherits the topological and measure-theoretic properties of the original windows.

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来源期刊

Indagationes Mathematicae-New Series 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

79 days

期刊介绍： Indagationes Mathematicae is a peer-reviewed international journal for the Mathematical Sciences of the Royal Dutch Mathematical Society. The journal aims at the publication of original mathematical research papers of high quality and of interest to a large segment of the mathematics community. The journal also welcomes the submission of review papers of high quality.