公除法拓扑中无处稠密集理想的一些性质

IF 0.6 3区数学 Q3 MATHEMATICS

Acta Mathematica Hungarica Pub Date : 2024-11-11 DOI:10.1007/s10474-024-01481-4

M. Kwela

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引用次数: 0

摘要

本文研究了共分拓扑中无处密集集的理想（Szyszkowska理想），并研究了它的一些基本性质。我们还探讨了所研究的理想与芙丝汀宝和丽扎的理想之间可能存在的包容性，从而回答了a . Nowik和P. Szyszkowska[17]最近的一篇文章中提出的开放性问题。此外，我们还讨论了Szyszkowska理想与一些在数论和组合学中起重要作用的著名理想之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Some properties of the ideal of nowhere dense sets in the common division topology

We consider the ideal of nowhere dense sets in the common division topology (Szyszkowska’s ideal), and examine some of its basic properties. We also explore the possible inclusions between the studied ideal and Furstenberg’s and Rizza’s ideals, thus answering open questions posed in a recent article by A. Nowik and P. Szyszkowska [17]. Moreover, we discuss the relationships of the Szyszkowska’s ideal with selected well-known ideals playing an important role in number theory and combinatorics.

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来源期刊

Acta Mathematica Hungarica 数学-数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

4-8 weeks

期刊介绍： Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.