Introduction to temporal topology

Volume 34, Issue 3, pp 205--216 https://dx.doi.org/10.22436/jmcs.034.03.01

Publication Date: March 07, 2024 Submission Date: January 22, 2024 Revision Date: February 04, 2024 Accteptance Date: February 06, 2024

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 521 Downloads
• 1590 Views

Authors

A. Mhemdi - Department of Mathematics, College of Sciences and Humanities in Aflaj, Prince Sattam bin Abdulaziz University, Riyadh, Saudi Arabia. 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, New Cairo, Egypt.

Abstract

Temporal topology studies chronological variation of the topology of an object (set). In this paper, we will present the basic definitions related to temporal topology. In addition, the classical continuity and separations axioms known in general topology will be generalized to temporal topological spaces. Also, we will show that the subcategory of temporal \(T_{0Q}\)-spaces is reflective in the category of temporal topological spaces. The necessary illustrative examples to elaborate on the obtained results and relationships are provided.

Share and Cite

Keywords

• Topological space
• operators of interior and closure
• continuity
• separation axioms
• category of \(T_0\)-space

MSC

•  54A05
•  54D10
•  18A40

References

• [1] T. M. Al-shami, Paracompactness on supra topological spaces, J. Linear Topol. Algebra, 9 (2020), 1–7
  • View Article
  • Google Scholar
  • MATH


• [2] 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


• [3] 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


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


• [5] 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


• [6] T. M. Al-shami, E. A. Abo-Tabl, B. A. Asaad, Investigation of limit points and separation axioms using supra -open sets, Missouri J. Math. Sci., 32 (2020), 171–187
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] T. M. Al-shami, I. Alshammari, Rough sets models inspired by supra-topology structures, Artif. Intell. Rev, 56 (2023), 6855–6883
  • View Article
  • Google Scholar


• [8] 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


• [9] 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


• [10] C. E. Aull, R. Lowen, Handbook of the History of General Topology, Kluwer Academic Publishers, Dordrecht (2001)
  • View Article
  • MathSciNet
  • Google Scholar


• [11] 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


• [12] 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


• [13] R. A. Hosny, B. A. Asaad, A. A. Azzam, T. M. Al-shami, Various topologies generated from Ej-neighbourhoods via ideals, Complexity, 2021 (2021), 11 pages
  • View Article
  • Google Scholar


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


• [15] E. F. Lashin, A. M. Kozae, A. A. Abo Khadra, T. Medhat, Rough set theory for topological spaces, Internat. J. Approx. Reason., 40 (2005), 35–43
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [16] S. Mac Lane, Categories for the working mathematician, Springer-Verlag, New York (1971)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A. Mhemdi, T. M. Al-shami, Functionally separation axioms on general topology, J. Math., 2021 (2021), 4 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [19] A. S. Salama, Sequences of topological near open and near closed sets with rough applications, , 34 (2020), 51–58
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] 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