商空间的一个模型

Q3 Mathematics

Topological Algebra and its Applications Pub Date : 2017-04-25 DOI:10.1515/taa-2017-0003

H. Hattab

{"title":"商空间的一个模型","authors":"H. Hattab","doi":"10.1515/taa-2017-0003","DOIUrl":null,"url":null,"abstract":"Abstract Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.","PeriodicalId":30611,"journal":{"name":"Topological Algebra and its Applications","volume":"5 1","pages":"13 - 18"},"PeriodicalIF":0.0000,"publicationDate":"2017-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/taa-2017-0003","citationCount":"0","resultStr":"{\"title\":\"A model of quotient spaces\",\"authors\":\"H. Hattab\",\"doi\":\"10.1515/taa-2017-0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.\",\"PeriodicalId\":30611,\"journal\":{\"name\":\"Topological Algebra and its Applications\",\"volume\":\"5 1\",\"pages\":\"13 - 18\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-04-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1515/taa-2017-0003\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topological Algebra and its Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1515/taa-2017-0003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topological Algebra and its Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/taa-2017-0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

摘要

摘要设R是拓扑空间E上的一个开放等价关系。我们在E上定义了一个新的等价关系ℜ××ℜ如果x的R轨迹的闭包等于y的R轨迹闭包，则商空间E/ℜ称为轨迹类空间。在本文中，我们证明了空间E/ℜξ是商空间E/R的一个简单模型。该模型可以提供有限模型。给出了同胚群的轨道空间和叶空间的一些应用。

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

A model of quotient spaces

Abstract Let R be an open equivalence relation on a topological space E. We define on E a new equivalence relation ̃ℜ̅ by x̃ ̃ℜ̅y if the closure of the R-trajectory of x is equal to the closure of the R-trajectory of y. The quotient space E/̃ ̃ℜ̅ is called the trajectory class space. In this paper, we show that the space E/̃ ̃ℜ̅ is a simple model of the quotient space E/R. This model can provide a finite model. Some applications to orbit spaces of groups of homeomorphisms and leaf spaces are given.

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

Topological Algebra and its Applications Mathematics-Algebra and Number Theory

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

24 weeks