منابع مشابه
Lattices of Convex Sets
If F 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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Properties of several sorts of lattices of convex subsets of Rn are examined. The lattice of convex sets containing the origin turns out, for n > 1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of Rn and the lattice of all convex subsets of R. The lattices of arbitrary, of open bounded, and of compact convex sets in Rn all satisfy the same identitie...
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In this paper, we generalize the classical duplication of intervals in lattices. Namely, we deal with partial duplication instead of complete convex subsets. We characterize those subsets that guarantee the result to still be a lattice. Moreover, we show that semi-distributive and extremal lattices can be encompassed by such construction where classical duplication fails.
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We give two sufficient conditions for the lattice Co(Rn, X) of relatively convex sets of 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.
متن کاملFUZZY CONVEX SUBALGEBRAS OF COMMUTATIVE RESIDUATED LATTICES
In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1977
ISSN: 0002-9947
DOI: 10.2307/1998003