Separation Axioms in Soft Bitopological Ordered Spaces

IF 0.2 Q4 MATHEMATICS
Salama Hussien Ali Shalil, Sobhy Ahmed Ali El-Sheikh, Shehab El Dean Ali Kandil
{"title":"Separation Axioms in Soft Bitopological Ordered Spaces","authors":"Salama Hussien Ali Shalil, Sobhy Ahmed Ali El-Sheikh, Shehab El Dean Ali Kandil","doi":"10.11648/j.pamj.20231205.11","DOIUrl":null,"url":null,"abstract":"This paper presents a comprehensive study on bi-ordered soft separation axioms applied to soft bitopological ordered spaces. The main focus of this research is to examine the properties, descriptions, and characteristics of these axioms. By exploring the relationships between these axioms and other properties of soft bitopological ordered spaces, this study expands our understanding of these spaces and their associated properties. Notably, significant findings are presented, establishing connections between the introduced bi-ordered axioms and properties such as soft bitopological and soft hereditary properties. The concepts of bi-ordered soft separation axioms, namely <i>PSTi</i> (resp. <img width=\"100\" height=\"15\" src=\"http://article.sciencepublishinggroup.com/journal/141/1411369/image001.png\" />)−ordered spaces, (where <i>i</i> = 0, 1, 2), are introduced and illustrated through relevant examples. These examples help clarify the relationships among the axioms and enhance our comprehension of their significance. Furthermore, this paper investigates the distinctions among separation axioms in topological ordered spaces and provides examples of relevant attributes from the literature. The separation axioms discussed in this research demonstrate enhanced descriptive power in characterizing the properties of topological ordered spaces. In addition to the above, the paper introduces the concept of bi-ordered subspace and explores the property of hereditary in the context of soft bitopological ordered spaces. These additions further enrich the understanding and applicability of bi-ordered soft separation axioms.","PeriodicalId":46057,"journal":{"name":"Italian Journal of Pure and Applied Mathematics","volume":"105 1","pages":"0"},"PeriodicalIF":0.2000,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Italian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.11648/j.pamj.20231205.11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

This paper presents a comprehensive study on bi-ordered soft separation axioms applied to soft bitopological ordered spaces. The main focus of this research is to examine the properties, descriptions, and characteristics of these axioms. By exploring the relationships between these axioms and other properties of soft bitopological ordered spaces, this study expands our understanding of these spaces and their associated properties. Notably, significant findings are presented, establishing connections between the introduced bi-ordered axioms and properties such as soft bitopological and soft hereditary properties. The concepts of bi-ordered soft separation axioms, namely PSTi (resp. Abstract Image)−ordered spaces, (where i = 0, 1, 2), are introduced and illustrated through relevant examples. These examples help clarify the relationships among the axioms and enhance our comprehension of their significance. Furthermore, this paper investigates the distinctions among separation axioms in topological ordered spaces and provides examples of relevant attributes from the literature. The separation axioms discussed in this research demonstrate enhanced descriptive power in characterizing the properties of topological ordered spaces. In addition to the above, the paper introduces the concept of bi-ordered subspace and explores the property of hereditary in the context of soft bitopological ordered spaces. These additions further enrich the understanding and applicability of bi-ordered soft separation axioms.
软双拓扑有序空间中的分离公理
本文全面研究了双序软分离公理在软双拓扑有序空间中的应用。本研究的主要重点是检验这些公理的性质、描述和特征。通过探索这些公理与软双拓扑有序空间其他性质之间的关系,本研究扩展了我们对软双拓扑有序空间及其相关性质的理解。值得注意的是,提出了重要的发现,建立了引入的双序公理和性质之间的联系,如软双拓扑和软遗传性质。双序软分离公理的概念,即PSTi (resp.)−有序空间(其中I = 0,1,2),通过相关示例进行介绍和说明。这些例子有助于澄清公理之间的关系,增强我们对其重要性的理解。进一步研究了拓扑有序空间中分离公理之间的区别,并从文献中给出了相关属性的例子。本文所讨论的分离公理在描述拓扑有序空间的性质方面表现出了较强的描述性。在此基础上,引入了双序子空间的概念,并在软双拓扑有序空间中探讨了遗传的性质。这些补充进一步丰富了双序软分离公理的理解和适用性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
0.60
自引率
0.00%
发文量
2
期刊介绍: The “Italian Journal of Pure and Applied Mathematics” publishes original research works containing significant results in the field of pure and applied mathematics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信