Let A and B be convex subsets in a finite-dimensional normed linear space X. A and B

Question:

Let A and B be convex subsets in a finite-dimensional normed linear space X. A and B can be strongly separated if and only if
P(A, B) = inf{||x - y|| : x ∈ A, y ∈ B} > 0
Combining proposition 3.14 with corollary 3.2.3 gives the following important result, a geometric form of the Hahn-Banach theorem (proposition 3.15).