Grill v - Space | Ibn AL-Haitham Journal For Pure and Applied Sciences

Authors

Rana Bahjat Esmaeel Department of Mathematics, College of Education for Pure Science Ibn- ALHaitham, University of Baghdad, Baghdad, Iraq https://orcid.org/0000-0002-4743-6034

DOI:

https://doi.org/10.30526/37.2.3789

Abstract

This scientific study aims to introduce a new type of topological space, called "Grill v-space", with the aim of contributing to scientific knowledge in this field. New generalizations were developed for both the local function and the Kuratowski closure function in order to generalize their concepts. Subsequently, these generalizations were used to define a new topology based on the concepts associated with the grill and the v -space. The set of v -open in v -space is defined as the sum of the set of v -open forms in v -space when the grill consists of the subsets of P(X) except the empty set. Many of the properties of this new space were demonstrated, and a number of illustrative examples were given.

References

Choquet, G. “Sur les notions de filtre et de grille,” Comptes Rendus Acad. Sci. Paris, 1947. 224, 171–173.

Thrown, K.; Chattopadhyay, W. Extensions of closure spaces. Can. J. Math, 1977, 29(6), 1277–1286.

Njasted, O.; Chattopadhyay, T. W. Merotopic spaces and extensions of closure spaces. Can. J. Math. 1983, 35, 613–629.

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

Mustafa, M. O.; Esmaeel, R. B. Some Properties in Grill–Topological Open and Closed Sets in Journal of Physics: Conference Series, 2021, 1897(1), 12038. https://doi.org/10.1088/1742-6596/1897/1/012038

Mustafa, M. O.; Esmaeel, R. B. Separation Axioms with Grill-Topological Open Set. In Journal of Physics: Conference Series. 2021, 1879(2), 22107. https://doi.org/10.1088/1742-6596/1879/2/022107

Suliman,S. S.; Esmaeel, R. B. Some Properties of Connectedness in Grill Topological Spaces. Ibn AL-Haitham J. Pure Appl. Sci. 2022 35(4), 213–219. https://doi.org/10.30526/35.4.2878

Sameer, Z. T. –v Open Set and Some Related Concepts. M.Sc. Thesis, University of Tikrit. 2022.

Kandil, A.; S. A. El-Sheikh; M. Abdelhakem; Shawqi A. Hazza. On ideals and grills in topological spaces. South Asian. 2015.

Esmaeel, R. B.; N. M. Shahadhuh On Grill- semi-p- Separation axioms. in AIP Conference proceeding 2023, 2414, 040077. https://doi.org/10.1063/5.0117064

Suliman, S. S.; Esmaeel, R. B. On some topological concepts via grill. Int. J. Nonlinear Anal. Appl. 2022, 13(1), 3765–3772. https://doi.org/10.22075/IJNAA.2022.6158

VibinSalimRaj, S.; Senthilkumaran, V.; Palaniappan, Y. On Contra G (gs) Continuous Functions in Grill Topological Spaces. Glob. J. Pure Appl. Math. 2021, 17(2), 333–342.

Thivagar, M. L.; Reilly, I. L.; Dasan, M. A.; Ramesh, V. Generalized open sets in grill N-topology. Appl. Gen. Topol. 2017, 18(2), 289–299. https://doi.org/10.4995/agt.2017.6797

Al-Omari, A.; Noiri, T. Decompositions of continuity via grills. Jordan J. Math. Stat. 2011, 4(1), 33–46.

Dasan, M. A.; Thivagar, M. L. New classes of grill N-topological sets and functions. Appl. Sci. 2021, 23, 17–28.

Ganesan, S. New type of micro grill topological spaces via micro grills and mGg-closed sets. Int. J. Anal. Exp. Model Anal. 2021, 12, 680–706.

Mandal, D.; Mukherjee, M.N. On a class of sets via grill: A decomposition of continuity. Analele ştiinţifice ale Universităţii" Ovidius" Constanţa. Seria Matematică 2012, 20(1), 307-316.

SARAVANAKUMAR, D.; KALAİVANİ, N. On Grill S P-Open Set in Grill Topological Spaces. Journal New Theory, 2018, 23, 85–92.

Roy, B.; Mukherjee, M. Ner. Concerning topologies induced by principal grills. An. Stiint. Univ. AL. I. Cuza Iasi. Mat.(NS). 2009, 55(2), 285–294.

Roy, B.; Mukherjee, M. N.; Ghosh, S. K. On a new operator based on a grill and its associated topology. Arab Jour. Math Sc. 2008, 14, 21–32.

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.

Saif, A.; Al-Hawmi, M.; Al-Refaei, B. On Gω-open sets in grill topological spaces. J. Adv. Math. Comput. Sci. 2020, 35(6), 132–143.

Azzam, A. A.; Hussein, S. S.; Osman, H. S. Compactness of topological spaces with grills. Ital. J. Pure Appl. Math. 2020, 44, 198–207.

Al-Omari, A.; Noiri, T. ON Ψ~ G-SETS IN GRILL TOPOLOGICAL SPACES. Filomat. 2011, 25(2), 187–196.

Kalaivani, N.; Rahman, K.F.U.; Cepová, L.; Cep, R." On Grill Sβ-Open Set in Grill Topological Spaces. Mathematics. 2022, 10(23), 4626. https://doi.org/10.3390/math10234626

Rodyna, A. Hosny; Abd El-latif, A. M. Soft G-Compactness in Soft Topological Spaces. Annals of Fuzzy Mathematics and Informatics. 2015, 11(6), 1-15.

Abd El-Latif, A.M.; Hosny, R.A. Some soft sets via soft grills. South Asian J Math, 2018, 8(1), 18-30.

Ali Akbar Estajia; Toktam Haghdadib. The Pointfree Version of Grills. Faculty of Sciences and Mathematics, University of Nis, Serbi. 2020, 34 (8). https://doi.org/10.2298/FIL2008667E

Rodyna Ahmed Hosny; Alaa Mohamed Abd El-Latif. Pre Open Soft Sets via Soft Grills. Journal of new theory. 2015, 8, 29-40.

Dhanabal SARAVANAKUMAR; Nagarajan KALAİVANİ. On Grill Sp-open Set In Grill Topological Spaces. Journal of New Theory. 2018, 23, 85-92.