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Compactness and Complete Distributivity for Commutative Subspace Lattices

Journal of the London Mathematical Society, 1990
In 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, 1994
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Completion and amalgamation of bounded distributive quasi lattices

Logic Journal of IGPL, 2010
In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a well-known idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras.
Alizadeh M   +2 more
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A generalization of completely distributive lattices

Algebra Universalis, 1990
Let 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, 1996
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On Raney's theorems for completely distributive complete lattices

Colloquium Mathematicum, 1988
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Uniformities on completely distributive lattices

1990
Summary: 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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