An observation on Krull and derived dimensions of some topological lattices

M. Rostami; Ilda I. Rodrigues

Displaying similar documents to “An observation on Krull and derived dimensions of some topological lattices”

$𝒵$ -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...

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...

Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Michael Pinsker (2007)

Fundamenta Mathematicae

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The clone lattice Cl(X) over an infinite set X is a complete algebraic lattice with $2^{| X |}$ compact elements. We show that every algebraic lattice with at most $2^{| X |}$ compact elements is a complete sublattice of Cl(X).

Characteristic vectors of unimodular lattices which represent two

Mark Gaulter (2007)

Journal de Théorie des Nombres de Bordeaux

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We improve the known upper bound of the dimension $n$ of an indecomposable unimodular lattice whose shadow has the third largest possible length, $n - 16$ .

Displaying similar documents to “An observation on Krull and derived dimensions of some topological lattices”

𝒵 -distributive function lattices

Lattices of Scott-closed sets

Algebraic lattices are complete sublattices of the clone lattice over an infinite set

Characteristic vectors of unimodular lattices which represent two

$𝒵$ -distributive function lattices