用布尔值空间方法研究比拓空间的分离公理和清醒度

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS Fuzzy Sets and Systems Pub Date : 2024-12-13 DOI:10.1016/j.fss.2024.109241

Jing He, Dexue Zhang

{"title":"用布尔值空间方法研究比拓空间的分离公理和清醒度","authors":"Jing He, Dexue Zhang","doi":"10.1016/j.fss.2024.109241","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A system of separation axioms is proposed making use of Boolean-valued specialization order of bitopological spaces; The relationship between d-sobriety of bitopological spaces proposed by Jung and Moshier and sobriety of fuzzy topological spaces is studied; A Hofmann-Mislove theorem for bitopological spaces is established.</div></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":"503 ","pages":"Article 109241"},"PeriodicalIF":3.2000,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Boolean-valued space approach to separation axioms and sobriety of bitopological spaces\",\"authors\":\"Jing He, Dexue Zhang\",\"doi\":\"10.1016/j.fss.2024.109241\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A system of separation axioms is proposed making use of Boolean-valued specialization order of bitopological spaces; The relationship between d-sobriety of bitopological spaces proposed by Jung and Moshier and sobriety of fuzzy topological spaces is studied; A Hofmann-Mislove theorem for bitopological spaces is established.</div></div>\",\"PeriodicalId\":55130,\"journal\":{\"name\":\"Fuzzy Sets and Systems\",\"volume\":\"503 \",\"pages\":\"Article 109241\"},\"PeriodicalIF\":3.2000,\"publicationDate\":\"2024-12-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fuzzy Sets and Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0165011424003877\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fuzzy Sets and Systems","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0165011424003877","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}

引用次数: 0

摘要

本文从模糊拓扑学的角度，通过将位拓扑空间与布尔四元代数中估值的拓扑空间相提并论，对位拓扑空间的分离公理和清醒度进行了研究。利用位元学空间的布尔值特化阶提出了分离公理系统；研究了 Jung 和 Moshier 提出的位元学空间的 d-清醒度与模糊拓扑空间的清醒度之间的关系；建立了位元学空间的霍夫曼-米斯洛夫定理。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A Boolean-valued space approach to separation axioms and sobriety of bitopological spaces

This paper presents a study of separation axioms and sobriety of bitopological spaces from the point of view of fuzzy topology via identifying bitopological spaces with topological spaces valued in the Boolean algebra of four elements. A system of separation axioms is proposed making use of Boolean-valued specialization order of bitopological spaces; The relationship between d-sobriety of bitopological spaces proposed by Jung and Moshier and sobriety of fuzzy topological spaces is studied; A Hofmann-Mislove theorem for bitopological spaces is established.

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

Fuzzy Sets and Systems 数学-计算机：理论方法

CiteScore

6.50

自引率

17.90%

发文量

321

审稿时长

6.1 months

期刊介绍： Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.