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- 저자 : Samer Al Ghour (검색결과 6 건)
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Soft Minimal Soft Sets and Soft Prehomogeneity in Soft Topological Spaces
Samer Al Ghour 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.3
In this paper, we give characterizations for soft minimal soft open sets in terms of the soft closure operator, and we conclude that soft subsets of soft minimal soft open sets are soft preopen sets. In addition to these, we define soft minimal soft sets and soft minimal soft preopen sets as two new classes of soft sets in soft topological spaces, and we define soft prehomogeneity as a new soft topological property. We give several relationships regarding these new notions and related known soft topological notions. We show that soft minimal soft preopen sets are soft points, and we prove that soft minimal soft sets with non-null soft interiors are soft minimal soft open sets. Moreover, we show that soft prehomogeneous soft topological space that has a soft minimal soft set is soft locally indiscrete. Also, we give several characterizations of soft locally indiscrete soft topological space in terms of soft minimal soft open sets, soft minimal soft sets, soft preopen sets, and soft prehomogeneity. We deal with correspondence between our new soft topological notions and their analogs topological ones. Finally, we raise six open questions.
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Soft ω*-Paracompactness in Soft Topological Spaces
Samer Al Ghour 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.1
In this study, we introduce a new concept in soft topological spaces, namely, soft ω-paracompactness, and we provide characterizations thereof. Its connection with other related concepts is also studied. In particular, we show that soft ω*-paracompactness and soft paracompactness are independent of each other. In addition, we study the soft ω*-paracompactness of the soft topological space generated by an indexed family of ω*-paracompact topological spaces.
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Soft ω-Continuity and Soft ωs-Continuity in Soft Topological Spaces
Samer Al Ghour 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.2
In this study, soft ω-continuity and soft ωs-continuity are introduced as two new classes ofsoft functions, and several characterizations of these concepts are given. It is proven that softω-continuity is weaker than soft continuity and that soft ωs-continuity lies strictly between softω-continuity and soft semi-continuity. Sufficient conditions are introduced for the equivalencebetween soft ωs-continuity and soft ω-continuity, as well as that between soft ωs-continuityand soft semi-continuity. Furthermore, composition theorems regarding soft ω-continuity andsoft ωs-continuity are given. Finally, the relationships between the generated soft topologicalspaces and induced topological spaces are studied.
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Strong Form of Soft Semi-Open Sets in Soft Topological Spaces
Samer Al Ghour 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.2
Soft ωs-open sets as a class of soft sets that lies strictly between soft open sets and soft semi-open sets is introduced. The natural properties of soft ωs-open sets are described. Using soft ωs-open sets, soft ωs-closure and soft ωs-interior as new soft operators are defined and investigated. Furthermore, the relationships regarding generated soft topological spaces and generated topological spaces are studied.
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Soft θ<SUB>ω</SUB>-Open Sets and Soft θ<SUB>ω</SUB> -Continuity
Samer Al Ghour 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.1
The soft θω-closure operator is defined as a new soft operator that lies strictly between the usual soft closure and the soft θ-closure. Sufficient conditions are provided for equivalence between the soft θω-closure and usual soft closure operators, and between the soft θω-closure and soft θ-closure operators. Via the soft θω-closure operator, the soft θω-open sets are defined as a new class of soft sets that lies strictly between the class of soft open sets and the class of soft θ-open sets. It is proven that the class of soft θω-open sets form a new soft topology. The soft θ-regularity is characterized via both the soft θω-closure operator and soft θω-open sets. The soft product theorem and several soft mapping theorems are introduced. The correspondence between the soft topology of the soft θω-open sets of soft topological space and their generated topological spaces, and vice versa, are studied. In addition to these, soft θω-continuity as a strong form of soft θ-continuity is introduced and investigated.
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Soft ωb-Openness and Soft b-Lindelofness
Samer Al Ghour 한국지능시스템학회 2023 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.23 No.2
In this study, we obtained several results regarding the soft ωb-open sets. For example, wedemonstrate that they form a soft supra topology that contains classes of soft ω-open setsand soft b-open sets. Additionally, using soft ωb-open sets, we define and investigate thesoft ωb-closure and soft ωb-interior as two new operators. Furthermore, we introduce andinvestigate soft b-antilocal countability as a novel soft-topological property. In addition, weintroduce quasi-soft b-openness and weakly quasi-soft b-openness as two new classes of softfunctions. Finally, we investigate the relationships between the new concepts and their analogsin a general topology.
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