On some weaker forms of soft continuity and their decomposition theorems

Volume 29, Issue 4, pp 317--328 https://doi.org/10.22436/jmcs.029.04.02
Publication Date: November 03, 2022 Submission Date: July 18, 2022 Revision Date: August 08, 2022 Accteptance Date: August 13, 2022

Authors

S. Al Ghour - Department of Mathematics and Statistics, Jordan University of Science and Technology, IRBID, Jordan.


Abstract

In this paper, we employ soft \(\omega ^{0}\)-open sets to establish four new classes of soft functions in STSs: soft \(\omega ^{0}\) -continuity, soft weak \(\omega ^{0}\)-continuity, soft \(w^{\ast }\) -continuity, and soft \(w^{\ast }\)-\(\omega ^{0}\)-continuity. We show that soft weak \(\omega ^{0}\)-continuity and soft \(w^{\ast }\)-\(\omega ^{0}\) -continuity are distinct notions, each of which is strictly weaker than soft \(\omega ^{0}\)-continuity. Furthermore, we get a soft \(\omega ^{0}\) -continuity decomposition theorem via both weak \(\omega ^{0}\)-continuity and soft \(w^{\ast }\)-\(\omega ^{0}\)-continuity. In addition, we demonstrate that soft \(w^{\ast }\)-continuity is precisely between soft continuity and soft \( w^{\ast }\)-\(\omega ^{0}\)-continuity. We further show that soft \(w^{\ast }\) -continuity and soft weak continuity are distinct concepts. In addition, we develop a soft continuity decomposition theorem via soft \(w^{\ast }\) -continuity and soft weak continuity. Finally, we examine the connection between our new soft topological ideas and their corresponding topological concepts. Include keywords, mathematical subject classification numbers as needed.


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ISRP Style

S. Al Ghour, On some weaker forms of soft continuity and their decomposition theorems, Journal of Mathematics and Computer Science, 29 (2023), no. 4, 317--328

AMA Style

Al Ghour S., On some weaker forms of soft continuity and their decomposition theorems. J Math Comput SCI-JM. (2023); 29(4):317--328

Chicago/Turabian Style

Al Ghour, S.. "On some weaker forms of soft continuity and their decomposition theorems." Journal of Mathematics and Computer Science, 29, no. 4 (2023): 317--328


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