g置换度空间的指标有界性和一致连通性

IF 0.6 Q3 MATHEMATICS

Applied general topology Pub Date : 2021-10-01 DOI:10.4995/agt.2021.15566

R. Beshimov, D. Georgiou, R. M. Zhuraev

{"title":"g置换度空间的指标有界性和一致连通性","authors":"R. Beshimov, D. Georgiou, R. M. Zhuraev","doi":"10.4995/agt.2021.15566","DOIUrl":null,"url":null,"abstract":"In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.","PeriodicalId":8046,"journal":{"name":"Applied general topology","volume":"71 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Index boundedness and uniform connectedness of space of the G-permutation degree\",\"authors\":\"R. Beshimov, D. Georgiou, R. M. Zhuraev\",\"doi\":\"10.4995/agt.2021.15566\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.\",\"PeriodicalId\":8046,\"journal\":{\"name\":\"Applied general topology\",\"volume\":\"71 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied general topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4995/agt.2021.15566\",\"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":"Applied general topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4995/agt.2021.15566","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: 6

摘要

在这篇论文中，g -报酬的空间退化，比如重量、uniform connection和指数波动。是proved that:(1)如果(X, U) a制服太空,然后是绘图πn n, G: X (s, U n)→(SP谷n GX, SP)是uniformly挑战和uniformly开放,而且w (U) = w (SP - n GU);(2)如果《绘图:f (X, Y)→(U, V)是a uniformly挑战(开放),然后绘图SP n女朋友:杂志》(SP谷n GX, SP)→(SP n运动,SP GV)是也uniformly挑战(开放);(3)如果《统一空间(X, U) uniformly连通,然后是制服太空(SP谷n GX, SP)是也uniformly连通。

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

Index boundedness and uniform connectedness of space of the G-permutation degree

In this paper the properties of space of the G-permutation degree, like: weight, uniform connectedness and index boundedness are studied. It is proved that:(1) If (X, U) is a uniform space, then the mapping π s n, G : (X n , U n ) → (SP n GX, SP n GU) is uniformly continuous and uniformly open, moreover w (U) = w (SP n GU);(2) If the mapping f : (X, U) → (Y, V) is a uniformly continuous (open), then the mapping SP n Gf : (SP n GX, SP n GU) → (SP n GY, SP n GV) is also uniformly continuous (open);(3) If the uniform space (X, U) is uniformly connected, then the uniform space (SP n GX, SP n GU) is also uniformly connected.

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

Applied general topology MATHEMATICS-

CiteScore

1.20

自引率

25.00%

发文量

审稿时长

15 weeks

期刊介绍： The international journal Applied General Topology publishes only original research papers related to the interactions between General Topology and other mathematical disciplines as well as topological results with applications to other areas of Science, and the development of topological theories of sufficiently general relevance to allow for future applications. Submissions are strictly refereed. Contributions, which should be in English, can be sent either to the appropriate member of the Editorial Board or to one of the Editors-in-Chief. All papers are reviewed in Mathematical Reviews and Zentralblatt für Mathematik.