A Convexity Structure Admits but One Real Linearization of Dimension Greater than One

@inproceedings{Meyer1973ACS,
title={A Convexity Structure Admits but One Real Linearization of Dimension Greater than One},
author={W. Meyer and David C. Kay},
year={1973}
}

If V is a vector space over an ordered field F and has algebraic operations + and o, these algebraic operations determine which subsets of V are convex. Now consider a set V with no algebraic structure, but with a convexity structure, that is, a family # of subsets of V which are closed under intersection. The determination of a linear structure (F, +, o) for V which makes V a vector space over a field F whose convex sets are precisely the members of # from properties of # alone has been called… CONTINUE READING