id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-3789	Esmaeel, Rana Bahjat	Grill v- Space	2024	8	.pdf	application/pdf	4192	311	88	= (𝒩 − 𝐴)𝑐⋃Υ𝕾((𝒩 − 𝐴)𝑐) = (𝒩𝑐 ∪ 𝐴) ∪ Υ𝕾(𝒩𝑐 ∪ 𝐴), now by Theorem 3.4(1) that 𝒱𝕾 − 𝑐𝑙(𝐺𝑐) = (𝒩𝑐 ∪ 𝐴) ∪ Υ𝕾(𝒩𝑐) ∪ Υ𝕾(𝐴). = {𝒩 − 𝐴: 𝒩 ∈ 𝒱𝑂𝑋 and 𝐴 ∉ 𝕾 } is a basis for 𝒱𝕾. Proof: Let Ɱ ∈ 𝒱𝕾 and 𝑥 ∈ Ɱ, then 𝑥 ∉ K − Ɱ, but	cache/iajs-3789.pdf	txt/iajs-3789.txt