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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
DOI: https://doi.org/10.1090/S0002-9947-1977-0463051-9
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.


References [Enhancements On Off] (What's this?)

  • [1] M. K. Bennett, On generating affine geometries, Algebra Universalis 4 (1974), 207-219. MR 50 #4417. MR 0351929 (50:4417)
  • [2] -, Coordinatization of affine and projective space, Discrete Math. 4 (1973), 219-231. MR 47 #948. MR 0312386 (47:948)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0463051-9
Article copyright: © Copyright 1977 American Mathematical Society

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