Bijections on the set of extreme points in a compact convex set

Anil Kumar Karn; Susmita Seal

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arXiv · 2605.20750

Bijections on the set of extreme points in a compact convex set

Anil Kumar Karn·Susmita Seal

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Abstract

In a recent work, Roelands and Tiersma proved that, for a compact convex set $K$, the space $A(K)$ of all real-valued continuous affine functions on $K$, is a JB-algebra if and only if there is a gauge-reversing bijection on $A_c(K)$, the set of positive real-valued continuous affine functions on $K$. In this paper, we show that every such gauge-reversing bijection on $A_c(K)$ is completely determined by the induced bijection on the set of extreme points of $K$.

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BibTeX RIS

Anil Kumar Karn, Susmita Seal. 2026-05-20. Bijections on the set of extreme points in a compact convex set. https://arxiv.org/abs/2605.20750

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