On the axiomatization of convex subsets of Banach spaces

Details On the axiomatization of convex subsets of Banach spaces On the axiomatization of convex subsets of Banach spaces

2011-05-06

arxiv.org/abs/1105.1270v2

Mathematics

Metric Geometry

8 pages, 1 figure, to appear in Proc. Amer. Math. Soc

Scientific paper

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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