Join-semidistributive lattices of relatively convex sets
Rings and Algebras
2011-06-15 v1 Metric Geometry
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.
Cite
@article{arxiv.math/0403104,
title = {Join-semidistributive lattices of relatively convex sets},
author = {K. Adaricheva},
journal= {arXiv preprint arXiv:math/0403104},
year = {2011}
}
Comments
11 pages, first presented on AAA-65 in Potsdam, March 2003