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arXiv · 1105.1270

On the axiomatization of convex subsets of Banach spaces

Valerio Capraro·Tobias Fritz
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Abstract

We prove that any convex-like structure in the sense of Nate Brown is affinely and isometrically isomorphic to a closed convex subset of a Banach space. This answers an open question of Brown. As an intermediate step, we identify Brown's algebraic axioms as equivalent to certain well-known axioms of abstract convexity. We conclude with a new characterization of convex subsets of Banach spaces.

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Valerio Capraro, Tobias Fritz. 2011-05-06. On the axiomatization of convex subsets of Banach spaces. https://doi.org/10.1090/s0002-9939-2013-11465-6

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