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Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both ext X and ext Y are Lindelöf spaces. We prove that if there exists an isomorphism T : A c (X) → A c (Y ) with T · T −1 < 2, then ext X is homeomorphic to ext Y . This generalizes results of C.doi:10.1090/s0002-9939-2010-10534-8 fatcat:46wsrhvmyjf3hfevvyf7gfcdh4