%0 Journal Article
%T Sublattices of lattices of convex subsets of vector spaces
%A Friedrich Wehrung
%A Marina V. Semenova
%J Mathematics
%D 2005
%I arXiv
%X For a left vector space V over a totally ordered division ring F, let Co(V) denote the lattice of convex subsets of V. We prove that every lattice L can be embedded into Co(V) for some left F-vector space V. Furthermore, if L is finite lower bounded, then V can be taken finite-dimensional, and L embeds into a finite lower bounded lattice of the form $Co(V,Z)=\{X\cap Z | X\in Co(V)\}$, for some finite subset $Z$ of $V$. In particular, we obtain a new universal class for finite lower bounded lattices.
%U http://arxiv.org/abs/math/0501324v1