The Dual Normal CHIP and Linear Regularity for Infinite Systems of Convex Sets in Banach Spaces

For an indexed collection of convex sets in a Banach space with index set $I$ of cardinality $|I|$ of $I$, which may be finite or infinite, we investigate the interrelationship between various qualification notions including the linear regularity, the normal property, the dual normal conical hull intersection property, and Jameson's property $(G)$, together with their quantitative versions, and thereby we extend the well-known results of Bakan, Deutsch, and Li [Trans. Amer. Math. Soc., 357 (2005), pp. 3831--3863], and Bauschke, Borwein, and Li [Math. Program. Ser. A, 86 (1999), pp. 135--160] from the finite case to the more general case that allows $|I|$ to be infinite.