  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.
