Results 191 to 200 of about 217 (205)
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Continuous and Completely Distributive Lattices
2014The study of continuous lattices was initiated by Dana Scott in the late 1960s in order to build mathematical models for certain constructs in theoretical computer science ([638] in LTF), and computational notions and motivations have continued to play a key role in the theory.
Klaus Keimel, Jimmie Lawson
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Distributive and completely distributive lattice extensions of ordered sets
International Journal of Algebra and Computation, 2018It is known that a poset can be embedded into a distributive lattice if, and only if, it satisfies the prime filter separation property. We describe here a class of “prime filter completions” for posets with the prime filter separation property that are completely distributive lattices generated by the poset and preserve existing finite meets and joins.
Wilmari Morton, Clint J. van Alten
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Compactness and Complete Distributivity for Commutative Subspace Lattices
Journal of the London Mathematical Society, 1990In this note, we show that if \({\mathcal L}\) is a commutative subspace lattice generated by a completely distributive lattice and finitely many commuting chains, then \({\mathcal L}\) is compact in the strong operator topology if and only if \({\mathcal L}\) is completely distributive.
Davidson, Kenneth R., Pitts, David R.
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Affine complete distributive lattices
Order, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A generalization of completely distributive lattices
Algebra Universalis, 1990Let A and B be subsets of the poset (P,\(\leq)\). A is said to be well below B, \(A\ll B\), if whenever D is a directed subset of P for which sup(D) exists and belongs to the upset \(\uparrow B\), one has that \(D\cap \uparrow A\neq \emptyset\). According to Gierz and Lawson, a lattice L is generalized continuous (a GCL), if one has for every x in L ...
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Affine completions of distributive lattices
Order, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Canonical extensions, free completely distributive lattices, and complete retracts
Algebra Universalis, 2021John Harding +2 more
exaly
Uniformities on completely distributive lattices
1990Summary: We extend the definition of uniformity in the form of a system of covers to completely distributive lattices and prove that uniformizability coincides with complete regularity on completely distributive lattice.
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