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On some topological concepts via grill | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3765-3772 اصل مقاله (331.35 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6158 | ||
| نویسندگان | ||
| Saad S. Suliman* ؛ R. B. Esmaeel | ||
| Department of Mathematics College of Education for Pure Science, Ibn Al-Haitham University of Baghdad, Iraq | ||
| تاریخ دریافت: 21 آذر 1400، تاریخ بازنگری: 17 دی 1400، تاریخ پذیرش: 14 بهمن 1400 | ||
| چکیده | ||
| In this work, the new grill concepts are studied using grill topological spaces and by using some defined sets where the set $\alpha$-open sets are defined. Properties of this set and some relationships were presented, in addition to studying a set of functions, including open, closed and continuous functions, finding the relationship between them and giving examples and properties that belong to this set, which will be a starting point for studying many topological properties using this set. | ||
| کلیدواژهها | ||
| Grill؛ $\alpha$-open sets؛ $\alpha$-closed sets؛ ₢*$\alpha$-open function؛ ₢*$\alpha$-c function | ||
| مراجع | ||
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[1] G. Choquet, Sur les notions de filtre et grille, Compt. Rend. Acad. Sci. Paris 224 (1947) 171–173. [2] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Month. 70 (1963) 36–41. [3] M.O. Mustafa and R.B. Esmaeel, Separation axioms with grill-topological open set, J. Phys. Conf. Ser. 1879(2) (2021) 022107. [4] M.O. Mustafa and R.B. Esmaeel, Some properties in grill-topological open and closed sets, J. Phys. Conf. Ser. 1897(1) (2021), 012038. [5] A.I. Nasir and R.B. Esmaeel, On α-J-space, JARDCS 11(1) (2019) 1379–1382. [6] B. Roy and M.N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math. 33(4) (2007) 771–786. [7] S.G. Saeed and R.B. Esmaeel, Separation axioms via αg-open set, J. Phys. Conf. Ser. 1591(1) (2020) 012099. [8] D. Saravanakumar and N. Kalaivani, On grill Sp-open set in grill topological spaces, J. New Theory 23 (2018) 85–92. | ||
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