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International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 183-192
Published online June 25, 2022
https://doi.org/10.5391/IJFIS.2022.22.2.183
© The Korean Institute of Intelligent Systems
Soft -Continuity and Soft -Continuity in Soft Topological Spaces
Samer Al Ghour
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
Correspondence to :
Samer Al Ghour (algore@just.edu.jo)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this study, soft ω-continuity and soft ωs-continuity are introduced as two new classes of soft functions, and several characterizations of these concepts are given. It is proven that soft ω-continuity is weaker than soft continuity and that soft ωs-continuity lies strictly between soft ω-continuity and soft semi-continuity. Sufficient conditions are introduced for the equivalence between soft ωs-continuity and soft ω-continuity, as well as that between soft ωs-continuity and soft semi-continuity. Furthermore, composition theorems regarding soft ω-continuity and soft ωs-continuity are given. Finally, the relationships between the generated soft topological spaces and induced topological spaces are studied.
Keywords: Soft semi-continuous functions, Soft ω-open sets, ω-continuity, ωs-continuity, Soft generated soft topological space, Soft induced topological spaces
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No potential conflict of interest relevant to this article was reported.
Biography
E-mail: algore@just.edu.jo
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Original Article
International Journal of Fuzzy Logic and Intelligent Systems 2022; 22(2): 183-192
Published online June 25, 2022 https://doi.org/10.5391/IJFIS.2022.22.2.183
Copyright © The Korean Institute of Intelligent Systems.
Soft -Continuity and Soft -Continuity in Soft Topological Spaces
Samer Al Ghour
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid, Jordan
Correspondence to:Samer Al Ghour (algore@just.edu.jo)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted noncommercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this study, soft ω-continuity and soft ωs-continuity are introduced as two new classes of soft functions, and several characterizations of these concepts are given. It is proven that soft ω-continuity is weaker than soft continuity and that soft ωs-continuity lies strictly between soft ω-continuity and soft semi-continuity. Sufficient conditions are introduced for the equivalence between soft ωs-continuity and soft ω-continuity, as well as that between soft ωs-continuity and soft semi-continuity. Furthermore, composition theorems regarding soft ω-continuity and soft ωs-continuity are given. Finally, the relationships between the generated soft topological spaces and induced topological spaces are studied.
Keywords: Soft semi-continuous functions, Soft ω-open sets, ω-continuity, ωs-continuity, Soft generated soft topological space, Soft induced topological spaces
