On the number of distributive lattices.

Erné, Marcel; Heitzig, Jobst; Reinhold, Jürgen

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On semimodular lattices of generating systems

Josef Dalík (1982)

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Lattices of generating systems

Josef Dalík (1980)

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$𝒵$ -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...