局部及物性

IF 0.6 4区数学 Q3 MATHEMATICS

Algebra Universalis Pub Date : 2022-06-28 DOI:10.1007/s00012-022-00783-4

Ali Akbar Estaji, Maryam Robat Sarpoushi, Ali Barzanouni

{"title":"局部及物性","authors":"Ali Akbar Estaji, Maryam Robat Sarpoushi, Ali Barzanouni","doi":"10.1007/s00012-022-00783-4","DOIUrl":null,"url":null,"abstract":"<div><p>For a dynamical system (<i>X</i>, <i>f</i>), the notion of <i>topological transitivity</i> has been studied by some researchers. There are several definitions of this property, and it is part of the folklore of dynamical systems that under some hypotheses, they are equivalent. In this paper, our aim is to introduce and study some properties of topological transitivity in pointfree topology, for which we first need to define in a way what makes them conservative extensions of topological transitivity defined by G.D. Birkhoff. We describe the way the different properties are related to each other in pointfree topology.</p></div>","PeriodicalId":50827,"journal":{"name":"Algebra Universalis","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Localic transitivity\",\"authors\":\"Ali Akbar Estaji, Maryam Robat Sarpoushi, Ali Barzanouni\",\"doi\":\"10.1007/s00012-022-00783-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>For a dynamical system (<i>X</i>, <i>f</i>), the notion of <i>topological transitivity</i> has been studied by some researchers. There are several definitions of this property, and it is part of the folklore of dynamical systems that under some hypotheses, they are equivalent. In this paper, our aim is to introduce and study some properties of topological transitivity in pointfree topology, for which we first need to define in a way what makes them conservative extensions of topological transitivity defined by G.D. Birkhoff. We describe the way the different properties are related to each other in pointfree topology.</p></div>\",\"PeriodicalId\":50827,\"journal\":{\"name\":\"Algebra Universalis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2022-06-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra Universalis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00012-022-00783-4\",\"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":"Algebra Universalis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00012-022-00783-4","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

对于一个动力系统（X，f），拓扑传递性的概念已经被一些研究者所研究。这种性质有几种定义，在一些假设下，它们是等价的，这是动力系统民间传说的一部分。在本文中，我们的目的是介绍和研究无点拓扑中拓扑传递性的一些性质，为此，我们首先需要定义一种使它们成为G.D.Birkhoff定义的拓扑传递性保守扩展的方法。我们描述了在无点拓扑中不同属性相互关联的方式。

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

Localic transitivity

For a dynamical system (X, f), the notion of topological transitivity has been studied by some researchers. There are several definitions of this property, and it is part of the folklore of dynamical systems that under some hypotheses, they are equivalent. In this paper, our aim is to introduce and study some properties of topological transitivity in pointfree topology, for which we first need to define in a way what makes them conservative extensions of topological transitivity defined by G.D. Birkhoff. We describe the way the different properties are related to each other in pointfree topology.

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

Algebra Universalis 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3 months

期刊介绍： Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.