On Nano Topological Spaces with Ideal Semi-p-open Sets
DOI:
https://doi.org/10.30526/38.3.3700Keywords:
NPO, NPC, NI-SPO sets, NI-SPC setsAbstract
The purpose of this paper is to introduce a new type of spaces called nano topological spaces and investigate the relation between nano topological space and nano ideal semi preopen set. The objective of this study is to develop a nano topological model. We study this model from three aspects, which are lower, upper approximation and their properties. Basic properties and characterizations related to these sets are given. And define the concept Nano ideal semi preopen set by using nano topological space and some properties of this set. The main aim of rough sets is to increase the accuracy measure and reduce the boundary region of sets by increasing the lower approximations and decreasing the upper approximations.
References
1. Mohammad RJ, Esmaeel RB. On separation axioms with soft-J-semi-g-open sets. IOP Conf Ser Mater Sci Eng 2020;871(1):012052. https://doi.org/10.1088/1757-899X/871/1/012052
2. Mahmoud BK, Yousif YY. Feeble Hausdorff spaces in alpha-topological spaces using graph. AIP Conf Proc 2022;2394(1). https://doi.org/10.1063/5.0121136
3. Esmaeel RB, Shahadhuh NM. Some results via Gril semi–p-open set. Ibn Al-Haitham J Pure Appl Sci 2021;34(4):108–115. https://doi.org/10.30526/34.4.2707
4. Nethaji O, Asokan R, Rajasekaran I. New generalized classes of an ideal nano topological spaces. Bull Int Math Virtual Inst 2019;9(3):543–552. https://doi.org/10.7251/BIMVI1903543N
5. Pawlak Z. Rough sets: Theoretical aspects of reasoning about data. Springer Sci Bus Media 2012.
6. Jafari S, Parimala M. On some new notions in nano ideal topological spaces. Eurasian Bull Math 2018;:85–93. https://www.researchgate.net/publication/329936077
7. Hosny RA, Al-Kadi D. Types of generalized open sets with ideal. Int J Comput Appl 2013;80(4). https://doi.org/10.5120/13848-1681
8. Jankovic D. Compatible extensions of ideals. Boll Un Mat Ital 1992;7:453–465. https://doi.org/10.4995/agt.2006.1932
9. Vaidyanathaswamy R. The localisation theory in set-topology. Proc Indian Acad Sci Sect A 1944;20:51–61. http://dx.doi.org/10.1007/BF03048958
10. Rajasekaran I, Nethaji O. Simple forms of nano open sets in an ideal nano topological space. J New Theory 2018;(24):35–43. https://dergipark.org.tr/en/pub/jnt/issue/38869/454517
11. Karim MA, Nasir AI. Some game via Ἷ-semi-g-separation axioms. Baghdad Sci J 2020;17(3):0861. https://doi.org/10.30526/33.1.2382
12. Mohamed AS, Esmaeel RB. On ƞǤ_Ş-compactness. Ibn Al-Haitham J Pure Appl Sci 2025;38(1):359–366. https://doi.org/10.30526/38.1.3322
13. Mahmoud BK, Yousif YY. Cut points and separations in alpha-connected topological spaces. Iraqi J Sci 2021;62(9):3091–3096. https://doi.org/10.24996/ijs.2021.62.9.24
14. Nasir NJ, Jabbar NA. Some types of compactness in bitopological spaces. Ibn Al-Haitham J Pure Appl Sci 2010;23(1). https://jih.uobaghdad.edu.iq/index.php/j/article/view/1000
15. Esmaeel RB, Mustafa MO. Separation axioms with grill-topological open set. J Phys Conf Ser 2021;1879(2):022107. https://doi.org/10.1088/1742-6596/1879/2/022107
16. smaeel RB, Mohammad RJ. On nano soft-ℐ-semi-g-closed sets. J Phys Conf Ser 2020;1591(1):012071. https://doi.org/10.1088/1742-6596/1591/1/012071
17. Thivagar ML, Richard C. On nano forms of weakly open sets. Int J Math Stat Invent 2013;1(1):31–37. https://www.researchgate.net/publication/276160426_On_Nano_Forms_Of_Weakly_Open_Sets
18. Thivagar ML, Jafari S, Devi VS. On new class of contra continuity in nano topology. Ital J Pure Appl Math 2017;41:1–2. https://ijpam.uniud.it/online_issue/202043/03%20Jafari-Thivagar-Devi.pdf
19. Esmaeel RB, Mustafa MO. On nano topological spaces with grill-generalized open and closed sets. AIP Conf Proc 2023;2414(1). https://doi.org/10.1063/5.0117062
20. Janković D, Hamlett TR. New topologies from old via ideals. Am Math Mon 1990;97(4):295–310. https://doi.org/10.1080/00029890.1990.11995593
21. Velicko NV. H-closed topological spaces. Am Math Soc Transl 1967;78(20):103–118. https://doi.org/10.1090/trans2/078/05
22. Rajasekaran I, Nethaji O. Simple forms of nano open sets in an ideal nano topological spaces. J New Theory 2018;(24):35–43. https://www.researchgate.net/publication/327100368_Simple_Forms_of_Nano_Open_Sets_in_an_Ideal_Nano_Topological_Spaces
23. Thivagar ML, Richard C. On nano forms of weakly open sets. Int J Math Stat Invent 2013;1(1):31–37. https://ijmsi.org/Papers/Version.1/E0111031037
24. Nasef AA, Aggour AI, Darwesh SM. On some classes of nearly open sets in nano topological spaces. J Egypt Math Soc 2016;24(4):585–589. https://doi.org/10.1016/j.joems.2016.01.008
25. Thivagar ML, Richard C. On nano continuity. Math Theory Model 2013;3(7):32–37. https://scirp.org/(S(i43dyn45teexjx455qlt3d2q))/reference/referencespapers.aspx?referenceid=3029056
26. Thivagar ML, Richard C. On nano continuity in a strong form. Int J Pure Appl Math 2015;101(5):893–904. https://www.researchgate.net/publication/276160411_On_Nano_Continuity
27. Reilly IL, Vamanamurthy. On α-sets in topological spaces. Tamkang J Math 1985;16:7–11. https://cyberleninka.org/article/n/377154
28. Thivagar ML, Devi VS. New sort of operators in nano ideal topology. Ultra Scientist 2016;28(1):51–64. https://www.ultrascientist.org/paper/44/new-sort-of-operators-in-nano-ideal-topology
29. Parimala M, Jafari S, Murali S. Nano ideal generalized closed sets in nano ideal topological spaces. Ann Univ Sci Budapest 2017;60:3–11. https://jit.ac.in/journal/Mathematics/4.pdf
30. Hussen RI, Salih HM. Ideal nano topological spaces with different subsets. J Phys Conf Ser 2021;1963(1):012120. https://doi.org/10.1088/1742-6596/1963/1/012120
31. Esmaeel RB, Nasir AI, Kalaf BA. On α-gĨ-closed soft sets. Sci Int (Lahore) 2018;30(5):703–705. https://www.researchgate.net/publication/327645156_ON_a-gI-_CLOSED_SOFT_SETS
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Ibn AL-Haitham Journal For Pure and Applied Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTermsHow to Cite
