Sublattices of lattices of convex subsets of vector spaces
نویسندگان
چکیده
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,Ω) = {X ∩Ω | X ∈ Co(V )}, for some finite subset Ω of V . In particular, we obtain a new universal class for finite lower bounded lattices.
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