# Join-semidistributive lattices of relatively convex sets

Source: [Join-semidistributive lattices of relatively convex sets](<https://www.sota2.com/research/paper/68fa4f311e209131ce96168a>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T10:10:47.064Z

Authors: K. Adaricheva

Published: 2004-03-05T06:12:21.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0403104>)

[PDF](<https://arxiv.org/pdf/math/0403104.pdf>)