Abstract
Let K and S be compact convex sets and let A(K) and A(S) be the corresponding Banach spaces of continuous affine functions. If the Banach-Mazur distance between A(K) and A(S) is less than 2, then under certain geometric conditions, the extreme boundaries of K and S are homeomorphic. This extends a result of Amir and Cambern and has applications to function algebras
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