{"title":"关于圆的 (a) 特征子群的一些评论","authors":"Nikola Bogdanovic","doi":"10.1016/j.topol.2024.109130","DOIUrl":null,"url":null,"abstract":"<div><div>In recent years, Barbieri, Dikranjan, Giordano Bruno and Weber have made progress on the problem of determining which characterized subgroups of the circle group are <em>(a-)factorizable</em>, that is, can be written as the sum of two proper (<em>a</em>-)characterized subgroups. We correct an imprecision in one of their results, <span><span>[2, Theorem 5.9]</span></span> from 2017, determining the countable <em>a</em>-characterized subgroups of <span><math><mi>T</mi></math></span> which are also <em>a</em>-factorizable. We also provide a revised proof of <span><span>[11, Proposition 1.3]</span></span> (Dikranjan, Kunen, 2007), asserting that <span><math><mi>Q</mi><mo>/</mo><mi>Z</mi></math></span> is characterized.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"359 ","pages":"Article 109130"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some remarks on (a)-characterized subgroups of the circle\",\"authors\":\"Nikola Bogdanovic\",\"doi\":\"10.1016/j.topol.2024.109130\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In recent years, Barbieri, Dikranjan, Giordano Bruno and Weber have made progress on the problem of determining which characterized subgroups of the circle group are <em>(a-)factorizable</em>, that is, can be written as the sum of two proper (<em>a</em>-)characterized subgroups. We correct an imprecision in one of their results, <span><span>[2, Theorem 5.9]</span></span> from 2017, determining the countable <em>a</em>-characterized subgroups of <span><math><mi>T</mi></math></span> which are also <em>a</em>-factorizable. We also provide a revised proof of <span><span>[11, Proposition 1.3]</span></span> (Dikranjan, Kunen, 2007), asserting that <span><math><mi>Q</mi><mo>/</mo><mi>Z</mi></math></span> is characterized.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"359 \",\"pages\":\"Article 109130\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-11-05\",\"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/S0166864124003158\",\"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/S0166864124003158","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
近年来，Barbieri、Dikranjan、Giordano Bruno 和 Weber 在确定圆组的哪些特征子群可（a-）因式分解，即可以写成两个适当的（a-）特征子群之和的问题上取得了进展。我们纠正了他们 2017 年的一个结果[2，定理 5.9]中的不精确之处，即确定 T 的可数 a 特征化子群也是可 a 因子化的。我们还对[11，命题 1.3]（Dikranjan，Kunen，2007）进行了修订证明，断言 Q/Z 是可表征的。
Some remarks on (a)-characterized subgroups of the circle
In recent years, Barbieri, Dikranjan, Giordano Bruno and Weber have made progress on the problem of determining which characterized subgroups of the circle group are (a-)factorizable, that is, can be written as the sum of two proper (a-)characterized subgroups. We correct an imprecision in one of their results, [2, Theorem 5.9] from 2017, determining the countable a-characterized subgroups of which are also a-factorizable. We also provide a revised proof of [11, Proposition 1.3] (Dikranjan, Kunen, 2007), asserting that is characterized.
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.
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