扩张行动和GCH

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-01-02 DOI:10.1016/j.topol.2024.109190

Luis Ferrari

{"title":"扩张行动和GCH","authors":"Luis Ferrari","doi":"10.1016/j.topol.2024.109190","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we provide a generalization in terms of actions of the theorem 2.2 in <span><span>[7]</span></span> establishing a necessary and sufficient condition for the existence of expansive homeomorphisms on countable compact spaces. The study of the cardinalities of groups acting expansively will lead us to a relationship between expansivity and the Generalized Continuum Hypothesis.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"361 ","pages":"Article 109190"},"PeriodicalIF":0.6000,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expansive actions and the GCH\",\"authors\":\"Luis Ferrari\",\"doi\":\"10.1016/j.topol.2024.109190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we provide a generalization in terms of actions of the theorem 2.2 in <span><span>[7]</span></span> establishing a necessary and sufficient condition for the existence of expansive homeomorphisms on countable compact spaces. The study of the cardinalities of groups acting expansively will lead us to a relationship between expansivity and the Generalized Continuum Hypothesis.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"361 \",\"pages\":\"Article 109190\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-01-02\",\"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/S0166864124003754\",\"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/S0166864124003754","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

本文对定理2.2在[7]中的作用进行了推广，建立了可数紧空间上可扩同胚存在的充分必要条件。研究扩张性群体的基数将使我们得到扩张性与广义连续统假设之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Expansive actions and the GCH

In this paper, we provide a generalization in terms of actions of the theorem 2.2 in [7] establishing a necessary and sufficient condition for the existence of expansive homeomorphisms on countable compact spaces. The study of the cardinalities of groups acting expansively will lead us to a relationship between expansivity and the Generalized Continuum Hypothesis.

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.