On Raney's theorems for completely distributive complete lattices
Gabriele H. Greco (1988)
Colloquium Mathematicae
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Gabriele H. Greco (1988)
Colloquium Mathematicae
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Marcin Łazarz (2019)
Bulletin of the Section of Logic
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Even if a lattice L is not distributive, it is still possible that for particular elements x, y, z ∈ L it holds (x∨y) ∧z = (x∧z) ∨ (y ∧z). If this is the case, we say that the triple (x, y, z) is distributive. In this note we provide some sufficient conditions for the distributivity of a given triple.
Janowitz, M.F., Coté, N.H. (1976)
Portugaliae mathematica
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Vinayak V. Joshi, B. N. Waphare (2005)
Mathematica Bohemica
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The concept of a 0-distributive poset is introduced. It is shown that a section semicomplemented poset is distributive if and only if it is 0-distributive. It is also proved that every pseudocomplemented poset is 0-distributive. Further, 0-distributive posets are characterized in terms of their ideal lattices.
Monteiro, Luiz, Abad, Manuel, Zander, Marta (2004)
Portugaliae Mathematica. Nova Série
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Zhang De-Xue (1997)
Commentationes Mathematicae Universitatis Carolinae
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The purpose of this paper is to study the topological properties of the interval topology on a completely distributive lattice. The main result is that a metrizable completely distributive lattice is an ANR if and only if it contains at most finite completely compact elements.
M. Lambrou (1983)
Fundamenta Mathematicae
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