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

Volume 25, Issue 2, pp 182--190 http://dx.doi.org/10.22436/jmcs.025.02.07
Publication Date: May 27, 2021 Submission Date: April 26, 2020 Revision Date: April 03, 2021 Accteptance Date: April 29, 2021

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.


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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


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