Vol. 24 No. 4 (2025): Mapana Journal of Sciences
Research Articles

Neutrosophic Nano Extremal Disconnectedness

  • K. Eswari,
  • V. Sutha Devi
K. Eswari
Department of Mathematics, Ayya Nadar Janaki Ammal College, Sivakasi - 626124, Tamil Nadu, India
V. Sutha Devi
Ayya Nadar Janaki Ammal College (Autonomous), Sivakasi-626124, Tamil Nadu, India

Published 2025-12-01

Keywords

  • NN -extremally disconnectedness,
  • NN -minimal structure,
  • NN -mixed space

Copyright (c) 2025

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Abstract

This paper delves into the exploration of extremally disconnected spaces within the context of neutrosophic nano topological space. It introduces a novel space termed neutrosophic nano mixed space, created through the fusion of neutrosophic nano minimal structure and neutrosophic nano topology. The primary objective is to investigate extremal disconnectedness within this new space, shedding light on its properties and implications. Furthermore, the research examines the characterization of various types of open sets within the neutrosophic nano mixed space. As an extension, we gave a bio-mathematical application of neutrosophic nano extremal disconnectedness.

References

  1. L. A. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8, pp. 338-353, 1965.
  2. K. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87-96, 1986.
  3. Smarandache.F, A unifying field in logics, neutrosophy: neutrosophic probability, set and logic, Rehoboth : American Research Press, 1998.
  4. Chang.C.L, “Fuzzy Topological Spaces,” Journal of Mathematical Analysis and Applications, vol. 24, pp. 182-190.
  5. Coker and Dogan, “An Introduction to intuitionistic fuzzy topological spaces,” Fuzzy Sets and Systems, vol. 88, no. 1, pp. 81-89, 1997.
  6. K. Serkan and K. Cemil, “Neutrosophic Topology,” Neutrosophic sets and Systems, vol. 13, pp. 90-95, 2016.
  7. L. Gillman and M. Jerison, Rings of continuous functions, New York: Univ.Series in Higher Math., Van Nostrand, Princeton, 1960.
  8. T. Lellis and R. Carmel, “On Nano Forms of Weakly Open sets,” Inter-nat.j.Math.and stat.Inv.,, vol. 1, no. 1, pp. 31-37, 2013.
  9. P. Gour, T. Binod Chandra and D. Runu, “On Continuity in Minimal Structure Neutrosophic Topological Space,” Neutrosophic Sets and Systems, vol. 51, pp. 360-370, 2022.
  10. A. Pandi, K. Banumathi and V. Vijeyarani, “Lies Between Nano Closed Sets And Nano g*-Closed Sets in Nano Minimal Structure Spaces,” International Journal of Research in Advent Technology, vol. 6, no. 10, pp. 2568-2572, 2018.
  11. A.-. O. Ahmad, A. S. Hanan and N. Takashi, “On extremally disconnected spaces via m-structure,” Commun.Korean Math.Soc., vol. 34, no. 1, pp. 351-359, 2019.
  12. M. Lellis Thivagar, J. Saeid , V. Sutha Devi and V. Antony Samy, “A novel approach to nano topology via neutrosophic sets,” Neutrosophic Sets and Systems, vol. 20, pp. 86-94, 2018.
  13. M. Lellis Thivagar, V. Ramesh and V. Antonysamy, “Extremally Disconnectedness in Nano Topology,” International Journal of Pure and Applied Mathematics, vol. 120, no. 8, pp. 197-205, 2018.
  14. T. Witczak, “Interior and closure in anti-minimal and anti-biminimal spaces in the frame of anti-topology,” Neutrosophic Sets and Systems, vol. 56, pp. 429-440, 2023.
  15. P. Gour, D. Runu and T. Binod Chandra , “Minimal Structures and Grill in Neutrosophic Topological Spaces,” Neutrosophic Sets and Systems, vol. 51, pp. 134-145, 2022.
  16. P. Kalaivani and R. Nithyakala, “An Application of Nano Topological Spaces in Agriculture,” International Journal of Scientific Research in Science and Technology, vol. 11, no. 5, pp. 292-300, 2024.
  17. A. Salama and S. Alblowi, “Generalized neutrosophic set and generalized neutrosophic topological spaces,” Journal of Computer Sci.Engineering, vol. 2, no. 7, pp. 129-132, 2012.