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Lattices of convex sets

Published:1977 Issue:1 Volume:234 Page:279-288
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Bennett Mary Katherine

Abstract

If V is a vector space over an ordered division ring, C a convex subset of V and L the lattice of convex subsets of C, then we call L a convexity lattice. We give necessary and sufficient conditions for an abstract lattice to be a convexity lattice in the finite dimensional case.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1977-234-01/S0002-9947-1977-0463051-9/S0002-9947-1977-0463051-9.pdf

Reference2 articles.

1. On generating affine geometries;Bennett, Mary Katherine;Algebra Universalis,1974

2. Coordinatization of affine and projective space;Bennett, Mary Katherine;Discrete Math.,1973

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Lattice of Convex Subsets of a Monounary Algebra;Bulletin of the Malaysian Mathematical Sciences Society;2017-01-11

2. Join-semidistributive lattices and convex geometries;Advances in Mathematics;2003-01

3. Parallel axiom in convexity lattices;Periodica Mathematica Hungarica;1992-02

4. Biatomic lattices;Algebra Universalis;1987-02

5. The convexity lattice of a poset;Order;1985-09

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