A New Weak* Closure Result for Normal Cones of subsets of Banach spaces

In this paper it is shown that if C and D are two closed convex subsets of a Banach space X and C ⋂D ⧣∅, then if x ∈ X, and A:= {v ∈ dom σ C∩D : (v, r) ∈ Epi σ C∩D} then N C∩D (x), the normal cone of C⋂D, is weak* closed whenever N C∩D (x) is a subset of A, where σC and NC are the support function and the normal cone of the set C respectively