Ri-separation axioms via supra soft topological spaces

Saleh, S.; Al-Shami, T. M.; Flaih, L. R.; Arar, M.; Abu-Gdairi, R.

doi:10.22436/jmcs.032.03.07

Cited by 3 publications

(1 citation statement)

References 32 publications

(34 reference statements)

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“…For instance, connectedness is a key point to prove the theorem of intermediate value, and compactness is a necessary condition to guarantee obtaining the maximum and minimum values for the continuous functions. Also, it is well known that separation axioms provide some categories for topological spaces [32,33] and help to prove some interesting properties of compactness and connectedness. With the goal of shedding light on the properties of separability in the framework of fuzzy topologies, we have written this article.…”

Section: Discussionmentioning

confidence: 99%

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Saleh,

Al-shami,

Azzam

et al. 2023

Mathematics

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It is common knowledge that fuzzy topology contributes to developing techniques to address real-life applications in various areas like information systems and optimal choices. The building blocks of fuzzy topology are fuzzy open sets, but other extended families of fuzzy open sets, like fuzzy pre-open sets, can contribute to the growth of fuzzy topology. In the present work, we create some classifications of fuzzy topologies which enable us to obtain several desirable features and relationships. At first, we introduce and analyze stronger forms of fuzzy pre-separation and regularity properties in fuzzy topology called fuzzy pre-Ti,i=0,12,1,2,3,4, fuzzy pre-symmetric, and fuzzy pre-Ri,i=0,1,2,3 by utilizing the concepts of fuzzy pre-open sets and quasi-coincident relation. We investigate more novel properties of these classes and uncover their unique characteristics. By presenting a wide array of related theorems and interconnections, we structure a comprehensive framework for understanding these classes and interrelationships with other separation axioms in this setting. Moreover, the relations between these classes and those in some induced topological structures are examined. Additionally, we explore the hereditary and harmonic properties of these classes.

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Section: Discussionmentioning

confidence: 99%

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Saleh,

Al-shami,

Azzam

et al. 2023

Mathematics

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Soft weakly connected sets and soft weakly connected components

Al-Ghour,

Al-Saadi

2023

MATH

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<abstract><p>Although the concept of connectedness may seem simple, it holds profound implications for topology and its applications. The concept of connectedness serves as a fundamental component in the Intermediate Value Theorem. Connectedness is significant in various applications, including geographic information systems, population modeling and robotics motion planning. Furthermore, connectedness plays a crucial role in distinguishing between different topological spaces. In this paper, we define soft weakly connected sets as a new class of soft sets that strictly contains the class of soft connected sets. We characterize this new class of sets by several methods. We explore various results related to soft subsets, supersets, unions, intersections and subspaces within the context of soft weakly connected sets. Additionally, we provide characterizations for soft weakly connected sets classified as soft pre-open, semi-open or $ \alpha $-open sets. Furthermore, we introduce the concept of a soft weakly connected component as follows: Given a soft point $ a_{x} $ in a soft topological space $ \left(X, \Delta, A\right) $, we define the soft weakly component of $ \left(X, \Delta, A\right) $ determined by $ a_{x} $ as the largest soft weakly connected set, with respect to the soft inclusion ($ \widetilde{\subseteq } $) relation, that contains $ a_{x} $. We demonstrate that the family of soft weakly components within a soft topological space comprises soft closed sets, forming a soft partition of the space. Lastly, we establish that soft weak connectedness is preserved under soft $ \alpha $-continuity.</p></abstract>

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New soft operators related to supra soft $ \delta_i $-open sets and applications

Abd El-latif,

Alqahtani

2024

MATH

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<abstract><p>This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.</p></abstract>

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Ri-separation axioms via supra soft topological spaces

Cited by 3 publications

References 32 publications

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Stronger Forms of Fuzzy Pre-Separation and Regularity Axioms via Fuzzy Topology

Soft weakly connected sets and soft weakly connected components

New soft operators related to supra soft $ \delta_i $-open sets and applications

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