id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2566	I. Abdullah, Norhan; K. Shaakir, Laith	Generalize partial Metric spaces	2020	13	.pdf	application/pdf	5541	270	90	𝐷𝑝( 𝛼, 𝛾, 𝛾) 𝑖𝑓 𝛽 = 𝛼 𝑇ℎ𝑒𝑛, 2𝐷𝑝( 𝛼, 𝛼, 𝛼) = 𝐷𝑝( 𝛼, 𝛼, 𝛼) + 𝐷𝑝( 𝛼, 𝛾, 𝛾) ⇒ 𝐷𝑝( 𝛼, 𝛼, 𝛼) = 𝐷𝑝(𝛼, 𝛾, 𝛾) … 11 𝐹𝑟𝑜𝑚 10&11, 𝑤𝑒 𝑔𝑒𝑡𝐷𝑝(𝛾, 𝛾, 𝛾) = 𝐷𝑝(𝛾, 𝛾, 𝛼) = 𝐷𝑝(𝛼, 𝛼, 𝛼) 𝑠𝑜 𝑏𝑦 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝛼 = 𝛾 … 12 𝑇ℎ𝑒𝑛 𝑏𝑦 9&12 𝑤𝑒 𝑔𝑒𝑡 𝛼 = 𝛽 = 𝛾. 3) 𝑇𝑟𝑖𝑣𝑖𝑎𝑙 4) 𝑏𝑦 𝑑𝑒𝑓𝑖𝑛𝑖𝑡𝑖𝑜𝑛 𝑠𝑖𝑛𝑐𝑒 𝐷𝑝(𝜇 , 𝜇 , 𝛽) + 𝐷𝑝(𝜇 , 𝜇 , 𝛾) For 𝛼 ∈ 𝑌 and 𝜖 > 0, the open ball of the general partial metric space with center 𝛼 and radius 𝜖 is 𝐵𝐷𝑝 (𝛼, 𝜖)	cache/iajs-2566.pdf	txt/iajs-2566.txt