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Some results for generalizations of semi-open sets in topological spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3803-3809 اصل مقاله (175.12 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.6165 | ||
| نویسندگان | ||
| Ali J. Mahmood* ؛ A. I. Naser | ||
| Department of Mathematics, College of Education for Pure Science, Ibn Al-Haitham University of Baghdad, Iraq | ||
| تاریخ دریافت: 19 آبان 1400، تاریخ بازنگری: 26 آذر 1400، تاریخ پذیرش: 28 دی 1400 | ||
| چکیده | ||
| This research generalized new types of semi-open sets using the concept of the grill and studied its properties, as well as the relationship between it and old concepts defined, as well as defining a new type of functions such as open and closed sets and determining the relationship between them, and providing many examples and properties that belong to this set, and this set will be a starting point to investigate the many futures of this set. | ||
| کلیدواژه‌ها | ||
| Grill؛ semi-open sets؛ semi-closed sets؛ ₲textsuperscript{*}-s-o function؛ ₲textsuperscript{*}-s-c function | ||
| مراجع | ||
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[1] A. Al-Omary and T. Noiri, Decomposition of continuity via grills, Jordan J. Math. Statist. 4(1) (2011) 33–46. [2] G. Choquet, Sur les notions de filtre et grille, Compt. Rend. Acad. Sci. Paris 224 (1947) 171–173. [3] R.B. Esmaeel and R.J Mohammad, On nano soft J-semi-g-closed sets, J. Phys. Conf. Ser. 159(1) (2020) 012071. [4] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer Math. Month. 70 (1963) 36–41. [5] M.O. Mustafa and R.B. Esmaeel, Separation axioms with grill-topological open set, J. Phys. Conf. Ser. 1879(2) (2021) 022107. [6] M.O. Mustafa and R.B. Esmaeel, Some properties in grill-topological open and closed sets, J. Phys. Conf. Ser. 1897(1) (2021), 012038. [7] B. Roy and M.N. Mukherjee, On a typical topology induced by a grill, Soochow J. Math. 33(4) (2007) 771–786. [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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