Join-semidistributive lattices of relatively convex sets

Abstract

We give two sufficient conditions for the lattice Co(R^n,X) of relatively convex sets of n-dimensional real space R^n to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice can be embedded into Co(R^n,X), for a suitable finite subset X of R^n.

11 pages, first presented on AAA-65 in Potsdam, March 2003

References in corpus (1)

• On lattices of convex sets in R^n

Cited by in corpus (3)

• Representing finite convex geometries by relatively convex sets
• On scattered convex geometries
• Sublattices of lattices of convex subsets of vector spaces