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arXiv · 2201.07671

Centre of a compact convex set

Anil Kumar Karn
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Abstract

We introduce the notion centre of a convex set and study the space of continuous affine functions on a compact convex set with a centre. We show that these spaces are precisely the dual of a base normed space in which the underlying base has a (unique) centre. We also characterize the corresponding base norm space. We obtain a condition on a compact, balanced, convex subset of a locally convex space so that the corresponding space of continuous affine functions on the convex set is an absolute order unit space. Similarly, we characterize a condition on the base with a centre of a base normed space so that the latter becomes an absolutely base normed space.

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Anil Kumar Karn. 2022-01-19. Centre of a compact convex set. https://arxiv.org/abs/2201.07671

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