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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)

Received: November 28, 2021; Revised: January 16, 2022; Accepted: January 26, 2022

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

No potential conflict of interest relevant to this article was reported.

Samer Al Ghour received his Ph.D. in Mathematics from the University of Jordan, Jordan in 1999. Currently, he is a professor in the Department of Mathematics and Statistics, Jordan University of Science and Technology, Jordan. His research interests include general topology, fuzzy topology, and soft set theory.

E-mail: algore@just.edu.jo


Article

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)

Received: November 28, 2021; Revised: January 16, 2022; Accepted: January 26, 2022

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

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