Join-semidistributive lattices of relatively convex sets
Abstract
We give two sufficient conditions for the lattice Co(Rn,X) of relatively convex sets of n-dimensional real space Rn 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(Rn,X), for a suitable finite subset X of Rn.
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