id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-6597	thabit, Sadeq; Alawadi, Alyaa; Noaman, Rafiqa	Collectionwise Pre-Normality in Topological Spaces	2025	15	.pdf	application/pdf	7825	453	79	(2) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of g⋆-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. (3) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of g-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. (4) for any discrete family {Fs}s∈S of closed sets in X, there exists a discrete family {Us}s∈S of πg-pre-open sets in X such that Fs ⊆ p int(Us) for each s ∈ S. Proof. Math, 18 (4) (2025), 6597 9 of 15 (2) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of pre-open sets in X such that p cl(Fs) ⊆ Us for each s ∈ S. (3) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of g⋆-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. (4) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of g-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. (5) for any discrete family {Fs}s∈S of g-closed sets in X, there exists a discrete family {Us}s∈S of πg-pre-open sets in X such that p cl(Fs) ⊆ p int(Us) for each s ∈ S. Proof.	cache/ejpam-6597.pdf	txt/ejpam-6597.txt