This is an announcement for the paper "On the axiomatization of convex subsets of Banach spaces" by Valerio Capraro, Tobias Fritz.

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.

Archive classification: math.MG math.FA math.OA

Mathematics Subject Classification: Primary 52A01, Secondary 46L36

Remarks: 8 pages, 1 figure

Submitted from: tobias.fritz@icfo.es

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1105.1270

or

http://arXiv.org/abs/1105.1270