Hrituraj Pal, Md Mirazul Hoque, B. Bhattacharya, J. Chakraborty
{"title":"A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space","authors":"Hrituraj Pal, Md Mirazul Hoque, B. Bhattacharya, J. Chakraborty","doi":"10.1515/jaa-2023-0163","DOIUrl":null,"url":null,"abstract":"Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.","PeriodicalId":44246,"journal":{"name":"Journal of Applied Analysis","volume":"2 3","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/jaa-2023-0163","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.
Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha].Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127-141].本文首先介绍混合模糊理想拓扑空间中的𝛿-ℐ-开盖。之后，我们介绍了𝛿-ℐ-紧密性，并讨论了其一些性质。研究表明，上述紧凑性是模糊紧凑性的弱形式。此外，我们还证明，如果我们重新拓扑模糊拓扑，那么在新的环境中，模糊𝛿-ℐ紧凑性和模糊紧凑性是等价的。此外，我们还引入了两种不同的连续性概念，并研究了模糊𝛿-ℐ紧凑性和模糊紧凑性之间的行为。
期刊介绍：
Journal of Applied Analysis is an international journal devoted to applications of mathematical analysis. Among them there are applications to economics (in particular finance and insurance), mathematical physics, mechanics and computer sciences. The journal also welcomes works showing connections between mathematical analysis and other domains of mathematics such as geometry, topology, logic and set theory. The journal is jointly produced by the Institute of Mathematics of the Technical University of Łódź and De Gruyter. Topics include: -applications of mathematical analysis (real and complex, harmonic, convex, variational)- differential equations- dynamical systems- optimization (linear, nonlinear, convex, nonsmooth, multicriterial)- optimal control- stochastic modeling and probability theory- numerical methods
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
