# $\theta_s$-open sets and $\theta_{s}$-continuity of maps in the product space

Volume 25, Issue 2, pp 182--190
Publication Date: May 27, 2021 Submission Date: April 26, 2020 Revision Date: April 03, 2021 Accteptance Date: April 29, 2021
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### Authors

Javier A. Hassan - Department of Mathematics $\&$ Statistics, College of Science $\&$ Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines. Mhelmar A. Labendia - Department of Mathematics $\&$ Statistics, College of Science $\&$ Mathematics, Mindanao State University-Iligan Institute of Technology, Iligan City, Philippines.

### Abstract

In this study, the concept of $\theta_s$-open set is introduced. The topology formed by $\theta_s$-open sets is strictly finer than the topology formed by $\theta$-open sets but is not comparable with the topology formed by $\omega_\theta$-open sets. Related concepts such as $\theta_s$-open and $\theta_s$-closed functions, $\theta_s$-continuous function, $\theta_s$-connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of $\theta_s$-continuous function from an arbitrary topological space into the product space is investigated further.

### Share and Cite

##### ISRP Style

Javier A. Hassan, Mhelmar A. Labendia, $\theta_s$-open sets and $\theta_{s}$-continuity of maps in the product space, Journal of Mathematics and Computer Science, 25 (2022), no. 2, 182--190

##### AMA Style

Hassan Javier A., Labendia Mhelmar A., $\theta_s$-open sets and $\theta_{s}$-continuity of maps in the product space. J Math Comput SCI-JM. (2022); 25(2):182--190

##### Chicago/Turabian Style

Hassan, Javier A., Labendia, Mhelmar A.. "$\theta_s$-open sets and $\theta_{s}$-continuity of maps in the product space." Journal of Mathematics and Computer Science, 25, no. 2 (2022): 182--190

### Keywords

• $\theta_s$-open
• $\theta_s$-closed
• $\theta_s$-connected
• $\theta_s$-continuous
• $\theta_s$-Hausdorff
• (\theta_s\)-regular
• $\theta_s$-normal

•  54A10
•  54A05