Displaying similar documents to “A note on convex sublattices of lattices”

Join-closed and meet-closed subsets in complete lattices

František Machala, Vladimír Slezák (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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To every subset A of a complete lattice L we assign subsets J ( A ) , M ( A ) and define join-closed and meet-closed sets in L . Some properties of such sets are proved. Join- and meet-closed sets in power-set lattices are characterized. The connections about join-independent (meet-independent) and join-closed (meet-closed) subsets are also presented in this paper.

Convex isomorphism of Q -lattices

Petr Emanovský (1993)

Mathematica Bohemica

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V. I. Marmazejev introduced in [3] the following concept: two lattices are convex isomorphic if their lattices of all convex sublattices are isomorphic. He also gave a necessary and sufficient condition under which the lattice are convex isomorphic, in particular for modular, distributive and complemented lattices. The aim this paper is to generalize this concept to the q -lattices defined in [2] and to characterize the convex isomorphic q -lattices.

Hypersubstitutions in orthomodular lattices

Ivan Chajda, Helmut Länger (2001)

Discussiones Mathematicae - General Algebra and Applications

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It is shown that in the variety of orthomodular lattices every hypersubstitution respecting all absorption laws either leaves the lattice operations unchanged or interchanges join and meet. Further, in a variety of lattices with an involutory antiautomorphism a semigroup generated by three involutory hypersubstitutions is described.

Stone Lattices

Adam Grabowski (2015)

Formalized Mathematics

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The article continues the formalization of the lattice theory (as structures with two binary operations, not in terms of ordering relations). In the paper, the notion of a pseudocomplement in a lattice is formally introduced in Mizar, and based on this we define the notion of the skeleton and the set of dense elements in a pseudocomplemented lattice, giving the meet-decomposition of arbitrary element of a lattice as the infimum of two elements: one belonging to the skeleton, and the...

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...