Generalized Kernel Sets via Ideals and the \(\widetilde{\Lambda}\)-Operator

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-24-2026-48
Published: Feb 26, 2026
Cite as:
Ibtesam Alshammari, Generalized Kernel Sets via Ideals and the \(\widetilde{\Lambda}\)-Operator, Int. J. Anal. Appl., 24 (2026), 48.

Main Article Content

Ibtesam Alshammari

Abstract

This work focuses on examining the properties of the co-local function set as defined in [1]. We define an operator \(\widetilde{\Lambda}\) using co-local function set  and investigate its various fundamental properties. Also, we introduce the notion of compatible kernel topology via ideal and obtain its characterizations along with several properties.

Article Details

References

  1. D. Jankovi?, T.R. Hamlett, New Topologies from Old via Ideals, Am. Math. Mon. 97 (1990), 295–310. https://doi.org/10.1080/00029890.1990.11995593.
  2. H. Maki, Generalized $Lambda$-Sets and the Associated Closure Operator, Special issue (1986), 139–146.
  3. F.G. Arenas, J. Dontchev, M. Ganster, On $lambda$-Sets and the Dual of Generalized Continuity, Quest. Answ. Gen. Topol. 15 (1997), 3–13.
  4. E. Khalimsky, R. Kopperman, P. R. Meyer, Computer Graphics and Connected Topologies on Finite Ordered Sets, Topol. Appl. 36 (1990), 1–17. https://doi.org/10.1016/0166-8641(90)90031-V.
  5. A.E.F. El Atik, A. Nasef, Topological Kernel of Sets and Application on Fractals, J. Contemp. Technol. Appl. Eng. 1 (2022), 1–8. https://doi.org/10.21608/jctae.2022.143392.1000.
  6. A. Al-Omari, M. Ozkoc, S. Acharjee, Primal-Proximity Spaces, Mathematica 66 (89) (2024), 151–167. https://doi.org/10.24193/mathcluj.2024.2.01.
  7. D. Mandal, M.N. Mukherjee, On Certain Types of Sets in Ideal Topological Spaces, Ann. West Univ. Timisoara - Math. Comput. Sci. 53 (2015), 99–108. https://doi.org/10.1515/awutm-2015-0017.
  8. E. Ekici, B. Roy, New Generalized Topologies on Generalized Topological Spaces Due to Csaszar, Acta Math. Hung. 132 (2010), 117–124. https://doi.org/10.1007/s10474-010-0050-6.
  9. J. Sanabria, L. Maza, E. Rosas, C. Carpintero, Generalized Kernels of Subsets Through Ideals in Topological Spaces, Iran. J. Math. Sci. Inform. 19 (2024), 207–221. https://doi.org/10.61186/ijmsi.19.2.207.
  10. R. Vaidyanathaswamy, The Localisation Theory in Set-Topology, Proc. Indian Acad. Sci. 20 (1944), 51–61. https://doi.org/10.1007/bf03048958.
  11. K. Kuratowski, Topology: Volume I, Academic Press, 1966.
  12. I. Alshammari, A. Al-Omari, Infra Cluster Topology via Infra Soft Topology and Ideal, J. Math. 2025 (2025), 8904772. https://doi.org/10.1155/jom/8904772.
  13. A. Al-Omari, O. Alghamdi, Regularity and Normality on Primal Spaces, AIMS Math. 9 (2024), 7662–7672. https://doi.org/10.3934/math.2024372.
  14. I. Alshammari, A. Al-Omari, On the Topology via Kernel Sets and Primal Spaces, Filomat 39 (2025), 6681–6692.
  15. A. Al-Omari, M.H. Alqahtani, Primal Structure with Closure Operators and Their Applications, Mathematics 11 (2023), 4946. https://doi.org/10.3390/math11244946.
  16. M. Mr?evi?, On Pairwise $R_0$ and Pairwise $R_1$ Bitopological Spaces, Bull. Math. Soc. Sci. Math. Repub. Socialiste Roum. 30 (1986), 141–148. https://www.jstor.org/stable/43681754.
  17. N.V. Veli?ko, $H$-Closed Topological Spaces, American Mathematical Society Translations: Series 2, American Mathematical Society, Providence, Rhode Island, 1968: pp. 103–118. https://doi.org/10.1090/trans2/078/05.
  18. A. Al-Omari, T. Noiri, Local Closure Functions in Ideal Topological Spaces, Novi Sad J. Math. 43 (2013), 139–149.
  19. R.L. Newcomb, Topologies Which Are Compact Modulo an Ideal, Ph.D. Dissertation, University of California at Santa Barbara, 1967.