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.
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 234 (1977), 279-288
- MSC: Primary 06A20; Secondary 52A20
- DOI: https://doi.org/10.1090/S0002-9947-1977-0463051-9
- MathSciNet review: 0463051