# On some weaker forms of soft continuity and their decomposition theorems

Volume 29, Issue 4, pp 317--328
Publication Date: November 03, 2022 Submission Date: July 18, 2022 Revision Date: August 08, 2022 Accteptance Date: August 13, 2022
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### 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.

### Share and Cite

##### 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

### Keywords

• Soft $\omega ^{0}$-openness
• soft continuity
• soft weak continuity
• generated soft topology

•  54C08
•  54C10
•  54B10