Displaying similar documents to “ 𝒵 -distributive function lattices”

Lattices of Scott-closed sets

Weng Kin Ho, Dong Sheng Zhao (2009)

Commentationes Mathematicae Universitatis Carolinae

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A dcpo P is continuous if and only if the lattice C ( P ) of all Scott-closed subsets of P is completely distributive. However, in the case where P is a non-continuous dcpo, little is known about the order structure of C ( P ) . In this paper, we study the order-theoretic properties of C ( P ) for general dcpo’s P . The main results are: (i) every C ( P ) is C-continuous; (ii) a complete lattice L is isomorphic to C ( P ) for a complete semilattice P if and only if L is weak-stably C-algebraic; (iii) for any two complete...

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.

Varieties of Distributive Rotational Lattices

Gábor Czédli, Ildikó V. Nagy (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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A rotational lattice is a structure 〈 L ; ∨ , ∧ , g 〉 where L = 〈 L ; ∨ , ∧ 〉 is a lattice and g is a lattice automorphism of finite order. We describe the subdirectly irreducible distributive rotational lattices. Using Jónsson’s lemma, this leads to a description of all varieties of distributive rotational lattices.

Radicals and complete distributivity in relatively normal lattices

Jiří Rachůnek (2003)

Mathematica Bohemica

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Lattices in the class ℐℛ𝒩 of algebraic, distributive lattices whose compact elements form relatively normal lattices are investigated. We deal mainly with the lattices in ℐℛ𝒩 the greatest element of which is compact. The distributive radicals of algebraic lattices are introduced and for the lattices in ℐℛ𝒩 with the sublattice of compact elements satisfying the conditional join-infinite distributive law they are compared with two other kinds of radicals. Connections between complete distributivity...