Lattices of convex sets
Author: Mary Katherine Bennett
Journal: Trans. Amer. Math. Soc. 234 (1977), 279-288
MSC: Primary 06A20; Secondary 52A20
MathSciNet review: 0463051
Abstract: If V is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.
-  Mary Katherine Bennett, On generating affine geometries, Algebra Universalis 4 (1974), 207–219. MR 0351929, https://doi.org/10.1007/BF02485726
-  Mary Katherine Bennett, Coordinatization of affine and projective space, Discrete Math. 4 (1973), 219–231. MR 0312386, https://doi.org/10.1016/S0012-365X(73)80003-2