Generalized \(\pi\)-weak closed sets and some applications on weak structures

Volume 31, Issue 3, pp 247--261 http://dx.doi.org/10.22436/jmcs.031.03.02

Publication Date: May 12, 2023 Submission Date: February 25, 2023 Revision Date: March 16, 2023 Accteptance Date: March 22, 2023

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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.

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Keywords

• Weak structure
• closed weak graph
• strongly closed weak graph
• separation axioms

MSC

•  54A05
•  54C08
•  54J05

References

• [1] P. Alexandroff, Diskrete R¨aume, Mat. Sbornik, 2 (1937), 501–519
  • View Article
  • Google Scholar


• [2] B. Almarri, A. A. Azzam, Energy Saving via a Minimal Structure, Math. Probl. Eng., 2022 (2022), 6 pages
  • View Article
  • Google Scholar


• [3] A. Al-Omari, T. Noiri, Weak continuity betweenWSS and GTS due to Cs´asz´ar, Malays. J. Math. Sci., 7 (2013), 297–313
  • View Article
  • Google Scholar


• [4] T. M. Al-shami, Somewhere dense sets and ST1-spaces, Punjab Univ. J. Math., 49 (2017), 101–111
  • View Article
  • Google Scholar


• [5] T. M. Al-shami, Supra semi-compactness via supra topological spaces, J. Taibah Univ. Sci., 12 (2018), 338–343
  • View Article
  • Google Scholar


• [6] T. M. Al-shami, Sum of the spaces on ordered setting, Morrocan J. Pure Appl. Anal., 6 (2020), 255–265
  • View Article
  • Google Scholar


• [7] T. M. Al-shami, Complete Hausdorffness and complete regularity on supra topological spaces, J. Appl. Math., 2021 (2021), 7 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] T. M. Al-shami, Improvement of the approximations and accuracy measure of a rough set using somewhere dense sets, Soft Comput., 25 (2021), 14449–14460
  • View Article
  • Google Scholar
  • MATH


• [9] T. M. Al-shami, New soft structure: Infra soft topological spaces, Math. Probl. Eng., 2021 (2021), 12 pages
  • View Article
  • Google Scholar


• [10] T. M. Al-shami, Topological approach to generate new rough set models, Complex Intell. Syst., 8 (2022), 4101–4113
  • View Article
  • Google Scholar


• [11] T. M. Al-shami, M. Abo-Elhamayel, Novel class of ordered separation axioms using limit points, Appl. Math. Inf. Sci., 14 (2020), 1103–1111
  • View Article
  • MathSciNet
  • Google Scholar


• [12] T. M. Al-shami, I. Alshammari, Rough sets models inspired by supra-topology structures, Artif. Intell. Rev., 56 (2022), 6855–6883
  • View Article
  • Google Scholar


• [13] T. M. Al-shami, M. E. El-Shafei, On supra soft topological ordered spaces, Arab J. Basic Appl. Sci., 26 (2019), 433–445
  • View Article
  • Google Scholar


• [14] T. M. Al-shami, A. Mhemdi, Approximation operators and accuracy measures of rough sets from an infra-topology view, Soft Comput., 27 (2023), 1317–1330
  • View Article
  • Google Scholar


• [15] T. M. Al-shami, T. Noiri, More notions and mappings via somewhere dense sets, Afr. Mat., 30 (2019), 1011–1024
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] T. M. Al-shami, T. Noiri, Compactness and Lindel¨ofness using somewhere dense and cs-dense sets, Novi Sad J. Math., 52 (2022), 165–176
  • View Article
  • Google Scholar


• [17] T. M. Al-shami, A. Rawshdeh, H. H. Al-jarrah, A. Mhemdi, Connectedness and covering properties via infra topologies with application to fixed point theorem, AIMS Math., 8 (2023), 8928–8948
  • View Article
  • MathSciNet
  • Google Scholar


• [18] A´ . Csa´sza´r, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357
  • View Article
  • MathSciNet
  • Google Scholar


• [19] A´ . Csa´sza´r, Weak structures, Acta Math. Hungar., 131 (2011), 193–195
  • View Article
  • MathSciNet
  • Google Scholar


• [20] M. M. El-Sharkasy, Minimal structure approximation space and some of its application, J. Intell. Fuzzy Syst., 40 (2021), 973–982
  • View Article
  • Google Scholar


• [21] M. E. El-Shafei, A. H. Zakari, T. M. Al-shami, Some applications of supra preopen sets, J. Math., 2020 (2020), 11 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [22] T. Husain, Topology and Maps, Plenum press, New York (1977)
  • View Article
  • Google Scholar


• [23] Y. K. Kim, W. Min, On weak structures and w-spaces, Far East J. Math. Sci., 97 (2015), 549–561
  • View Article
  • Google Scholar


• [24] E. Korczak-Kubiak, A. Loranty, R. J. Pawlak, Baire generalized topological spaces, generalized metric spaces and infinite games, Acta Math. Hungar., 140 (2013), 203–231
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [25] A. M. Kozae, M. Shokry, M. Zidan, Supra topologies for digital plane, AASCIT Communications, 3 (2016), 1–10
  • View Article
  • Google Scholar


• [26] P. E. Long, L. L. Herrington, Functions with strongly closed graph, Boll. Un. Mat. Ital., 12 (1975), 381–384
  • View Article
  • Google Scholar


• [27] H. Maki, On generalizing semi-open and preopen sets, In: Report for Meeting on Topological Spaces Theory and its Applications, Yatsushiro College of Technology, (1996), 13–18
  • View Article


• [28] A. S. Mashhour, A. A. Allam, F. S. Mahmoud, F. H. Kheder, On supra topological spaces, Indian J. Pure Appl. Math., 14 (1983), 502–510
  • View Article


• [29] A. Mhemdi, T. M. Al-shami, Functionally separation axioms on general topology, J. Math., 2021 (2021), 5 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [30] S. Modak, Dense sets in weak structure and minimal structure, Commun. Korean Math. Soc., 28 (2013), 589–596
  • View Article
  • MathSciNet
  • Google Scholar


• [31] H. Mustafa, T. M. Al-shami, R. Wassef, Rough set paradigms via containment neighborhoods and ideals, Filomat, 37 (2023), 4683–4702
  • View Article
  • Google Scholar


• [32] R. J. Pawlak, A. Loranty, The generalized entropy in the generalized topological spaces, Topology Appl., 159 (2012), 1734–1742
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [33] A. S. Salama, Topological solution for missing attribute values in incomplete information tables, Inf. Sci., 180 (2010), 631–639
  • View Article
  • Google Scholar


• [34] H. Soldano, A modal view on abstract learning and reasoning, In: Ninth Symposium on Abstraction, Reformulation, and Approximation, SARA, (2011), 7 pages
  • View Article
  • Google Scholar


• [35] B. K. Tyagi, H. V. S. Chauhan, On generalized closed sets in generalized topological spaces, Cubo, 18 (2016), 27–45
  • View Article


• [36] S. Yan, W. Yu, Formal verification of a topological spatial relations model for geographic information systems in Coq, Mathematics, 11 (2023), 1–18
  • View Article
  • Google Scholar


• [37] A. M. Zahran, K. El-Saady, A. Ghareeb, Modification of weak structures via hereditary classes, Appl. Math. Lett., 25 (2012), 869–872
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [38] A. M. Zahran, A. Ghareeb, A. K. Mousa, Almost continuity and its applications on weak structures, Afr. Mat., 28 (2017), 831–839
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [39] A. M. Zahran, A. K. Mousa, A. Ghareeb, Generalized closed sets and some separation axioms on weak structure, Hacet. J. Math. Stat., 44 (2015), 669–677
  • View Article
  • Google Scholar
  • MATH