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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Lattices of convex sets


Author: Mary Katherine Bennett
Journal: Trans. Amer. Math. Soc. 234 (1977), 279-288
MSC: Primary 06A20; Secondary 52A20
MathSciNet review: 0463051
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1977-0463051-9
PII: S 0002-9947(1977)0463051-9
Article copyright: © Copyright 1977 American Mathematical Society