Sublattices of lattices of convex subsets of vector spaces

Simple item page
dc.creatorWehrung, Friedrich
dc.creatorSemenova, Marina V.
dc.date2005-01-20
dc.date.accessioned2026-07-07T05:16:13Z
dc.date.available2026-07-07T05:16:13Z
dc.descriptionFor 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.
dc.identifierhttps://arxiv.org/abs/math/0501324
dc.identifierhttp://arxiv.org/abs/math/0501324
dc.identifierAlgebra and Logic 43, no. 3 (May-June 2004) (2004) 145--161
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/73902
dc.subjectGeneral Mathematics
dc.subject06B15, 52C10
dc.titleSublattices of lattices of convex subsets of vector spaces
dc.typetext

Files

Collections

arXiv