New generalized closure operators induced by local functions via ideals

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.

کلیدواژه ها:

Ideal ، (\cdot)^{\bullet}-operator ، \coprod^{\bullet}-operator ، generalized topology