Isomorphisms of spaces of continuous affine functions on compact convex sets with Lindelöf boundaries

Pavel Ludvík, Jiří Spurný
2011 Proceedings of the American Mathematical Society  
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 H. B. Cohen and C. H. Chu. 2000 Mathematics Subject Classification. 46A55, 46E15, 54D20.
doi:10.1090/s0002-9939-2010-10534-8 fatcat:46wsrhvmyjf3hfevvyf7gfcdh4