New generalized closure operators induced by local functions via ideals

Abass, Salah El-Din; Khiamy, Hossam Mahmoud; El-Sanowsy, E.; Ibedou, Ismail

doi:10.22103/jmmr.2025.24116.1703

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	New generalized closure operators induced by local functions via ideals
Journal of Mahani Mathematical Research
دوره 14، شماره 2 - شماره پیاپی 32، مرداد 2025، صفحه 221-243 اصل مقاله (538.38 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2025.24116.1703
نویسندگان
Salah El-Din Abass¹؛ Hossam Mahmoud Khiamy^* ¹؛ E. El-Sanowsy¹؛ Ismail Ibedou²
¹Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt
²Mathematics Department, Faculty of Science, Benha University, Benha 13518, Egypt
چکیده
This work aims to introduce and examine four new operators based on the topological structure “ideal” and the notion of “generalized” generating two generalized ideal topological spaces. The proposed structures are discussed in detail in terms of topological properties and some basic theories. Moreover, we obtain bases for the generated generalized ideal topological spaces. Further, we define the concept of topology suitable for an ideal. In addition, we provide several essential findings pertaining to these novel frameworks. We also provide several counterexamples that are related to our findings.
کلیدواژه‌ها
ideal؛ $(\cdot)^{\bullet}$-operator؛ $\coprod^{\bullet}$-operator؛ generalized topology

مراجع
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New generalized closure operators induced by local functions via ideals