TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Micro topological space with grill-generalized open sets

* , ,

* Corresponding author · click or hover a name for details

pp. 1439–1447Vol. 26Issue 7October 2023DOI: 10.47974/JIM-1562XML
Published Online:
28 Oct 2023
Article type:
Research Article
Language:
EN
Article no.:
JIM-1562
Pages:
1439–1447

Abstract

In the present paper, we define the concept of micro-Gg-open and micro-Gg-closed sets by using micro topological space, and several properties of that set are studied, so we introduce micro-Ggγ-open set and micro-Ggϖ- closed set and denoted of micro-Gg-open set by mic-GgO(U), micro-Gg-closed set by mic-GgC(U) several theories that true and examples to the contrary are not true. We also studied a practical example of a micro-Gg-open set and a micro-Gg-closed set.

Keywords

Subject Classifications

54A0554A99

References

[1] G. Choquet, Sur les notions de filter et grille, Comptes Rendus Comptes Rendus Acad. Sci. Paris, 224, pp. 171-173 (1947).
[2] M.L. Thivagar and C.Richard, On nano forms of weakly open sets. International Journal of Mathematics and Statistics Invention, 1(1), 31-37 (2013).
[3] S. Chandrasekar, On micro topological spaces. Journal of New Theory, (26), pp. 23-31 (2019).
[4] R.B. Esmaeel and M.O. Mustafa, On Nano Topological Spaces with Grill-Generalized Open and Closed Sets, Submitted.
[5] H.Z. Ibrahim, Strong forms of generalized closed sets in topological texture spaces, Journal of Advanced Studies in Topology, 6(2), pp. 61-68 (2015).
[6] H.Z. Ibrahim, On micro T1/2 space, International Journal of  Applied  Mathematics, 33(3), pp. 369-384, (2020).
[7] A.B. Khalaf and Hariwan Z. Ibrahim, Some applications of γ-P-open sets in topological spaces, International Journal of  Applied  Mathematical Sciences, 5(1-2), pp. 81- 369-384 (2011).
[8] A.B. Khalaf and Hariwan Z. Ibrahim, On some separation axioms via  β-γ-open sets, Gen. Math. Notes, 15(2), pp. 14-31 (2013).
[9] M. Parimala, and S. Jafari, On some new notions in nano ideal topological spaces. Eurasian Bulletin of Mathematics, pp. 85-93, (2018).
[10] Z. Pawlak, Rough Sets, International Journal of Computer and Information Sciences, 11, pp. 341-356 (1982).
[11] Hameed, Z. N., & Kadhem, H. H. : On Degree Topology and Set-T_0 space. Wasit Journal of Computer and Mathematics Sciences, 1(4), 213-219 (2022).
[12] Raju A. Muneshwar & Kirankumar L. Bondar. Open subset inclusion graph of a topological space, Journal of Discrete Mathematical Sciences and Cryptography, 22:6, 1007-1018 (2019), DOI: 10.1080/09720529.2019.1649029. 
[13] Yuming Feng & Benxiu Li. Generalized Hyperoperations Defined on Topological Space, Journal of Discrete Mathematical Sciences and Cryptography, 18:3, 195-200 (2015), DOI: 10.1080/09720529.2013.876779. 

Views: 282Downloads: 88Citations: 0