Displaying similar documents to “Free Q -distributive lattice over an n -element chain.”

Metrizable completely distributive lattices

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.

𝒵 -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

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It is known that for a nonempty topological space X and a nonsingleton complete lattice Y endowed with the Scott topology, the partially ordered set [ X , Y ] of all continuous functions from X into Y is a continuous lattice if and only if both Y and the open set lattice 𝒪 X are continuous lattices. This result extends to certain classes of 𝒵 -distributive lattices, where 𝒵 is a subset system replacing the system 𝒟 of all directed subsets (for which the 𝒟 -distributive complete lattices are just...