Generalized \(\pi\)-weak closed sets and some applications on weak structures
Authors
R. A. Hosny
- Department of Mathematics, Zagazig University, Zagazig, Egypt.
T. M. Al-Shami
- Department of Mathematics, Sana'a University, P.O. Box 1247, Sana'a, Yemen.
- Department of Engineering Mathematics \(\&\) Physics, Faculty of Engineering \(\&\) Technology, Future University, Egypt.
R. Abu-Gdairi
- Department of Mathematics, Faculty of Science, Zarqa University, P.O. Box 13110 Zarqa, Jordan.
A. Mhemdi
- Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia.
Abstract
This article highlights the concept of generalized \(\pi\)-weak closed sets (briefly, \(g\pi(w)\)-closed) in weak structures, that possess a lot of applications in information systems. We study their master properties and show the interrelationships between them and some types of sets with the help of counterexamples. Then, we applied \(g\pi(w)\)-closed sets to define new types of the concepts of separation axioms, continuous functions, closed \(w\)-graph and strongly closed \(w\)-graph. We give some characterizations of these concepts and discuss main features. Moreover, we provide some examples to show some topological properties of these concepts that are losing in the frame of weak structures.
Share and Cite
ISRP Style
R. A. Hosny, T. M. Al-Shami, R. Abu-Gdairi, A. Mhemdi, Generalized \(\pi\)-weak closed sets and some applications on weak structures, Journal of Mathematics and Computer Science, 31 (2023), no. 3, 247--261
AMA Style
Hosny R. A., Al-Shami T. M., Abu-Gdairi R., Mhemdi A., Generalized \(\pi\)-weak closed sets and some applications on weak structures. J Math Comput SCI-JM. (2023); 31(3):247--261
Chicago/Turabian Style
Hosny, R. A., Al-Shami, T. M., Abu-Gdairi, R., Mhemdi, A.. "Generalized \(\pi\)-weak closed sets and some applications on weak structures." Journal of Mathematics and Computer Science, 31, no. 3 (2023): 247--261
Keywords
- Weak structure
- closed weak graph
- strongly closed weak graph
- separation axioms
MSC
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