On ƞǤ_Ş-Compactness

Ahmed Sh. Mohamed; R.B. Esmaeel

doi:10.30526/38.1.3322

Authors

Ahmed Sh. Mohamed Department of Mathematics, College of Education for PurHaitham, University of Baghdad, Iraq.
R.B. Esmaeel Department of Mathematics, College of Education for Pure Science (Ibn Al Haitham), University of Baghdad, Baghdad, Iraq. https://orcid.org/0000-0002-4743-6034

DOI:

https://doi.org/10.30526/38.1.3322

Keywords:

Nano Grill semi-open compact space, ƞǤ_Ş Ỏ-semi-open compact, nano compact

Abstract

Open sets may be viewed as an extension of semi-open sets by applying the notions of semi-open sets and grill nano to nGs-open sets, with the following four goals in mind: The objective is to characterize nGs-open sets by examining and proving numerous of its attributes and comments. And investigate and define new kinds of functions based on the concept of nGs-open sets, using sets of nGs-open sets, we will define a new type of Compact type and call it nGs-open compact then we will find the relationship between these new types of Compact type with nano compact. We will also talk about the relationship between nano grill semi-open sets and continuous functions and the relationship between nano grill semi-open sets and irresolute function as well we give some examples, proofs and observations about the relationship between nano grill semi-open sets and functions and their relation to nano compact.

Author Biography

R.B. Esmaeel, Department of Mathematics, College of Education for Pure Science (Ibn Al Haitham), University of Baghdad, Baghdad, Iraq.

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References

1. Choquet G. Sur les notions de filtre et de grille. Comptes Rendus Acad Sci Paris. 1947;224:171-3.

2. Al-Omari A, Noiri T. Decomposition of continuity via grilles. Jordan J Math Stat. 2011;4(1):33-46.

3. Mustafa MO, Esmaeel RB. Some properties in grill–topological open and closed sets. J Phys Conf Ser. 2021;012038. https://doi.org/10.1088/1742-6596/1879/1/012038.

4. Choquet G. Sur les notions de filtre et de grille. Comptes Rendus Acad Sci Paris. 1947;224:171-3.

5. Crossley SG. Semi-closure. Texas J Sci. 1971;22:99-112.

6. Levine N. Generalized closed sets in topology. Rend Circ Mat Palermo. 1970;19:89-96.

7. Thivagar ML, Richard C. On nano forms of weakly open sets. Int J Math Stat Invent. 2013;1(1):31-7.

8. Thron WJ. Proximity structures and grills. Math Ann. 1973;206:35-62.

9. Mahmood AJ, Naser AI. Connectedness via generalizations of semi-open sets. Ibn AL-Haitham J Pure Appl Sci. 2022;35(4):235-40.

10. Suliman SS, Esmaeel RB. Some properties of connectedness in grill topological spaces. Ibn AL-Haitham J Pure Appl Sci. 2022;35(4):213-9.

11. Roy B, Mukherjee MN. On a typical topology induced by a grill. Soochow J Math. 2007;33(4):771.

12. Mandal D, Mukherjee MN. On a class of sets via grill: A decomposition of continuity. An Stiint Univ Ovidius Constanta Ser Mat. 2012;20(1):307-16.

13. Pawlak Z. Rough sets. Int J Comput Inf Sci. 1982;11:341-56. https://doi.org/10.1007/BF01001956

14. Esmaeel RB, Saeed SG. Nano αg Ị-open set. J Phys Conf Ser. 2021;012031. https://doi.org/10.1088/1742-6596/1879/1/012031

15. Hatir E, Jafari S. On some new classes of sets and a new decomposition of continuity via grills. J Adv Math Stud. 2010;3(1):33-41.

16. Njåstad O. On some classes of nearly open sets. Pac J Math. 1965;15(3):961-70.

17 . Noori S, Yousif YY. Soft simply compact spaces. Iraqi J Sci. 2020;108-13.

18 . Krishnaprakash S, Ramesh R, Suresh R. Nano-compactness and nano-connectedness in nano topological spaces. Int J Pure Appl Math. 2018;119(13):107-15.

19 . Noori S, Yousif YY. Soft simply compact spaces. Iraqi J Sci. 2020;108-13.

20 . Ryll-Nardzewski C. A remark on the Cartesian product of two compact spaces. Bull Acad Polon Sci Cl III. 1954;2:265-6.