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

New generalized closure operators induced by local functions via ideals

Document Type : Research Paper

Authors

Salah El-Din Abass ¹

Hossam Mahmoud Khiamy ¹

E. El-Sanowsy ¹

Ismail Ibedou ²

¹ Mathematics Department, Faculty of Science, Sohag University, Sohag 82524, Egypt

² Mathematics Department, Faculty of Science, Benha University, Benha 13518, Egypt

10.22103/jmmr.2025.24116.1703

Abstract

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.

Keywords

ideal

$(\cdot)^{\bullet}$-operator

$\coprod^{\bullet}$-operator

generalized topology

Subjects

Geometry and Topology

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