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. 
)−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.
| Published in | Pure and Applied Mathematics Journal (Volume 12, Issue 5) |
| DOI | 10.11648/j.pamj.20231205.11 |
| Page(s) | 79-85 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Soft Set, Soft Singleton, Bi−ordered Soft Separation Axioms, Bi−ordered Subspace, Hereditary Property
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APA Style
Salama Hussien Ali Shalil, Sobhy Ahmed Ali El-Sheikh, Shehab El Dean Ali Kandil. (2023). Separation Axioms in Soft Bitopological Ordered Spaces. Pure and Applied Mathematics Journal, 12(5), 79-85. https://doi.org/10.11648/j.pamj.20231205.11
ACS Style
Salama Hussien Ali Shalil; Sobhy Ahmed Ali El-Sheikh; Shehab El Dean Ali Kandil. Separation Axioms in Soft Bitopological Ordered Spaces. Pure Appl. Math. J. 2023, 12(5), 79-85. doi: 10.11648/j.pamj.20231205.11
AMA Style
Salama Hussien Ali Shalil, Sobhy Ahmed Ali El-Sheikh, Shehab El Dean Ali Kandil. Separation Axioms in Soft Bitopological Ordered Spaces. Pure Appl Math J. 2023;12(5):79-85. doi: 10.11648/j.pamj.20231205.11
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Download@article{10.11648/j.pamj.20231205.11,
author = {Salama Hussien Ali Shalil and Sobhy Ahmed Ali El-Sheikh and Shehab El Dean Ali Kandil},
title = {Separation Axioms in Soft Bitopological Ordered Spaces},
journal = {Pure and Applied Mathematics Journal},
volume = {12},
number = {5},
pages = {79-85},
doi = {10.11648/j.pamj.20231205.11},
url = {https://doi.org/10.11648/j.pamj.20231205.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20231205.11},
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. )−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.},
year = {2023}
}
TY - JOUR T1 - Separation Axioms in Soft Bitopological Ordered Spaces AU - Salama Hussien Ali Shalil AU - Sobhy Ahmed Ali El-Sheikh AU - Shehab El Dean Ali Kandil Y1 - 2023/09/27 PY - 2023 N1 - https://doi.org/10.11648/j.pamj.20231205.11 DO - 10.11648/j.pamj.20231205.11 T2 - Pure and Applied Mathematics Journal JF - Pure and Applied Mathematics Journal JO - Pure and Applied Mathematics Journal SP - 79 EP - 85 PB - Science Publishing Group SN - 2326-9812 UR - https://doi.org/10.11648/j.pamj.20231205.11 AB - 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. )−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. VL - 12 IS - 5 ER -
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