  Let X be a compact convex set and let ext X stand for the set of extreme
points of X. We show that an affine function with the point of continuity
property on X satisfies the minimum principle. As a corollary we obtain a
generalization of a theorem by H.B. Cohen and C.H. Chu by proving the following
result. Let X,Y be compact convex sets such that every extreme point of X and Y
is a weak peak point and let the Banach-Mazur distance between spaces of affine
continuous functions on X and Y is smaller then 2. Then ext X is homeomorphic
to ext Y.
