Join-closed and meet-closed subsets in complete lattices

František Machala; Vladimír Slezák

Displaying similar documents to “Join-closed and meet-closed subsets in complete lattices”

An extension of the ordering based on nullnorms

Emel Aşıcı (2019)

Kybernetika

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In this paper, we generally study an order induced by nullnorms on bounded lattices. We investigate monotonicity property of nullnorms on bounded lattices with respect to the $F$ -partial order. Also, we introduce the set of incomparable elements with respect to the F-partial order for any nullnorm on a bounded lattice. Finally, we investigate the relationship between the order induced by a nullnorm and the distributivity property for nullnorms.

Construction methods for uni-nullnorms and null-uninorms on bounded lattice

Ümit Ertuğrul, M. Nesibe Kesicioğlu, Funda Karaçal (2019)

Kybernetika

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In this paper, two construction methods have been proposed for uni-nullnorms on any bounded lattices. The difference between these two construction methods and the difference from the existing construction methods have been demonstrated and supported by an example. Moreover, the relationship between our construction methods and the existing construction methods for uninorms and nullnorms on bounded lattices are investigated. The charactertics of null-uninorms on bounded lattice $L$ are...

Lattice-inadmissible incidence structures

Frantisek Machala, Vladimír Slezák (2004)

Discussiones Mathematicae - General Algebra and Applications

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Join-independent and meet-independent sets in complete lattices were defined in [6]. According to [6], to each complete lattice (L,≤) and a cardinal number p one can assign (in a unique way) an incidence structure $J_{L}^{p}$ of independent sets of (L,≤). In this paper some lattice-inadmissible incidence structures are founded, i.e. such incidence structures that are not isomorphic to any incidence structure $J_{L}^{p}$ .

On covariety lattices

Tomasz Brengos (2008)

Discussiones Mathematicae - General Algebra and Applications

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This paper shows basic properties of covariety lattices. Such lattices are shown to be infinitely distributive. The covariety lattice $L_{C V} (K)$ of subcovarieties of a covariety K of F-coalgebras, where F:Set → Set preserves arbitrary intersections is isomorphic to the lattice of subcoalgebras of a $P_{κ}$ -coalgebra for some cardinal κ. A full description of the covariety lattice of Id-coalgebras is given. For any topology τ there exist a bounded functor F:Set → Set and a covariety K of F-coalgebras,...

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...