  In this paper, we study different kinds of normal properties for infinite
system of arbitrarily many convex sets in a Banach space and provide the dual
characterization for the normal property in terms of the extended Jamenson
property for arbitrarily many weak*-closed convex cones in the dual space.
Then, we use the normal property and the extended Jamenson property to study
CHIP, strong CHIP and linear regularity for the infinite case of arbitrarily
many convex sets and establish equivalent relationship among these properties.
In particular, we extend main results in [3] on normal property, Jamenson
property, CHIP and linear regularity for finite system of convex sets in a
Hilbert space to the infinite case of arbitrarily many convex sets in Banach
space setting.
