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arXiv · 1801.07940

The minimum principle for affine functions with the point of continuity property and isomorphisms of spaces of continuous affine function

Petr Dostál·Jiří Spurný
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Abstract

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.

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Petr Dostál, Jiří Spurný. 2018-01-24. The minimum principle for affine functions with the point of continuity property and isomorphisms of spaces of continuous affine function. https://arxiv.org/abs/1801.07940

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