具有递增子序列的序列

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-08-26 DOI:10.1016/j.topol.2024.109049

Łukasz Mazurkiewicz, Szymon Żeberski

{"title":"具有递增子序列的序列","authors":"Łukasz Mazurkiewicz, Szymon Żeberski","doi":"10.1016/j.topol.2024.109049","DOIUrl":null,"url":null,"abstract":"<div><p>We study analytic and Borel subsets defined similarly to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e. division. It consists of sequences which contain increasing subsequence in given order.</p><p>We consider a variety of sets defined in a similar way. Some of them occurs to be Borel subsets of the Baire space, while others are analytic complete, hence not Borel.</p><p>In particular, we show that an analogon of Luzin example based on the natural linear order on rationals is analytic complete. We also characterize all countable linear orders having such property.</p></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"356 ","pages":"Article 109049"},"PeriodicalIF":0.6000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sequences with increasing subsequence\",\"authors\":\"Łukasz Mazurkiewicz, Szymon Żeberski\",\"doi\":\"10.1016/j.topol.2024.109049\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study analytic and Borel subsets defined similarly to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e. division. It consists of sequences which contain increasing subsequence in given order.</p><p>We consider a variety of sets defined in a similar way. Some of them occurs to be Borel subsets of the Baire space, while others are analytic complete, hence not Borel.</p><p>In particular, we show that an analogon of Luzin example based on the natural linear order on rationals is analytic complete. We also characterize all countable linear orders having such property.</p></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"356 \",\"pages\":\"Article 109049\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864124002347\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864124002347","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究的解析子集和玻尔子集的定义与卢津给出的解析完全集的老例子类似。卢津的例子本质上是拜尔空间的一个子集，它基于自然数的自然偏序，即除法。它由按给定顺序包含递增子序列的序列组成。我们考虑了以类似方式定义的各种集合，其中有些集合是贝叶尔空间的贝叶尔子集，而另一些则是解析完全集，因此不是贝叶尔集。我们还描述了具有这种性质的所有可数线性阶的特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Sequences with increasing subsequence

We study analytic and Borel subsets defined similarly to the old example of analytic complete set given by Luzin. Luzin's example, which is essentially a subset of the Baire space, is based on the natural partial order on naturals, i.e. division. It consists of sequences which contain increasing subsequence in given order.

We consider a variety of sets defined in a similar way. Some of them occurs to be Borel subsets of the Baire space, while others are analytic complete, hence not Borel.

In particular, we show that an analogon of Luzin example based on the natural linear order on rationals is analytic complete. We also characterize all countable linear orders having such property.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.