id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5732	Sama-ae, Areeyuth; Boonpok, Chawalit 	Characterizations of  $\delta_1\text{-}{\beta}_{\mathcal{I}}$-paracompactness concerning an ideal	2025	13	.pdf	application/pdf	6890	457	79	I : U ∈ τ and I ∈ I}. Since (X, τ∗, I) is δ1-βI-paracompact, U has τ∗-locally finite refinement V = {Gλ : λ ∈ Λ2} of open sets in (X, τ∗, I) such that X − ∪{Gλ : λ ∈ Λ2} ∈ I, where Gλ = Vλ − Iλ, Vλ ∈ τ and	cache/ejpam-5732.pdf	txt/ejpam-5732.txt