On ƞǤ_Ş-Compactness - Sh. Mohamed , Ahmed; Esmaeel, R.B. (Ibn AL-Haitham Journal For Pure and Applied Sciences, 2025)
Open sets may be viewed as an extension of semi-open sets by applying the notions of semi-open sets and grill nano to nGs-open sets, with the following four goals in mind: The objective is to characterize nGs-open sets by examining and proving numerous of its attributes and comments. And investigate and define new kinds of functions based on the concept of nGs-open sets, using sets of nGs-open sets, we will define a new  type of Compact type and call it nGs-open compact then we will find the relationship between these new types of Compact type with nano compact. We will also talk about the relationship between nano grill semi-open sets and continuous functions and the relationship between nano grill semi-open sets and irresolute function as well we give some examples, proofs and observations about the relationship between nano grill semi-open sets and functions and their relation to nano compact.