Nigh-Open Sets in Topological Space

Main Article Content

Jamal Oudetallah, Nabeela Abu-Alkishik, Iqbal M. Batiha

Abstract

In this paper, we aim to introduce a new class of open sets namely nigh-open set. Accordingly, we define a topological space called a nigh-topological space. This consequently leads us to outline several new operations in connection with the sets in nigh-topological space coupled with deriving several their properties and relations.

Article Details

References

  1. H.A. Shehadeh, I.H. Jebril, X. Wang, S.C. Chu, M.Y.I. Idris, Optimal Topology Planning of Electromagnetic Waves Communication Network for Underwater Sensors Using Multi-Objective Optimization Algorithms (MOOAs), Automatika. 64 (2022), 315-326. https://doi.org/10.1080/00051144.2022.2123761.
  2. R.A. Hosny, B.A. Asaad, A.A. Azzam, T.M. Al-Shami, Various Topologies Generated from Ej-Neighbourhoods via Ideals, Complexity. 2021 (2021), 4149368. https://doi.org/10.1155/2021/4149368.
  3. A.S. Salama, A. Mhemdi, O.G. Elbarbary, T.M. Al-shami, Topological Approaches for Rough Continuous Functions with Applications, Complexity. 2021 (2021), 5586187. https://doi.org/10.1155/2021/5586187.
  4. J. Oudetallah, Countably and Locally Compactness in Bitopological Spaces, Gen. Lett. Math. 12 (2022), 148-153. https://doi.org/10.31559/glm2022.12.3.5.
  5. J. Oudetallah, M.M. Rousan, I.M. Batiha, On D-Metacompactness in Topological Spaces, J. Appl. Math. Inform. 39 (2021), 919-926.
  6. J. Oudetallah, I.M. Batiha, On Almost Expandability in Bitopological Spaces, Int. J. Open Problems Compt. Math. 14 (2021), 43-48.
  7. A. A. Hnaif, A. A. Tamimi, A. M. Abdalla, I. Jebril, A Fault-Handling Method for the Hamiltonian Cycle in the Hypercube Topology, Comput. Mater. Contin. 68 (2021), 505-519. https://doi.org/10.32604/cmc.2021.016123.
  8. J. Oudetallah, I.M. Batiha, Mappings and Finite Product of Pairwise Expandable Spaces, Int. J. Anal. Appl. 20 (2022), 66. https://doi.org/10.28924/2291-8639-20-2022-66.
  9. J. Oudetallah, R. Alharbi, I.M. Batiha, On r-Compactness in Topological and Bitopological Spaces, Axioms. 12 (2023), 210. https://doi.org/10.3390/axioms12020210.
  10. J.L. Kelley, General Topology, Springer, New York, 1955.
  11. J. Dugundji, Topology, Allyn and Bacon, Boston, 1966.
  12. N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. Math. Mon. 70 (1963), 36-41. https://doi.org/10.1080/00029890.1963.11990039.