id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5570	Boonpok, Chawalit ; Sama-ae, Areeyuth; Raktaow, Palin 	Characterizations of Generalized Paracompactness in Ideal Topological Spaces	2025	12	.pdf	application/pdf	6562	444	81	For every closed subset F of X and every x ̸∈ F , there exist disjoint δ-βI-open sets U and V such that x ∈ U and F − V ∈ I. (ii) As F − ∪{Wy : y ∈ F} = F − (∪{Wy : y ∈ F} ∪ {G}) ⊂ X − (∪{Wy : y ∈ F} ∪ {G}), we get that F −∪{Wy : y ∈ F} ∈ I. It follows that V = ∪{Wy : y ∈ F} is a δ-βI-open set in X and F − V ∈ I.	cache/ejpam-5570.pdf	txt/ejpam-5570.txt