Vladimír Slezák (2001)
Discussiones Mathematicae - General Algebra and Applications
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In this paper the context of independent sets is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.
Richard Valent (1973)
Colloquium Mathematicae
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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 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 .
Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu (2019)
Kybernetika
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In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on from the t-norm on a subinterval of need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other...
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 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 -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,...
Antonio Boccuto, Xenofon Dimitriou (2019)
Kybernetika
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Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.
Kamila Kliś-Garlicka (2016)
Czechoslovak Mathematical Journal
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The notion of a bilattice was introduced by Shulman. A bilattice is a subspace analogue for a lattice. In this work the definition of hyperreflexivity for bilattices is given and studied. We give some general results concerning this notion. To a given lattice we can construct the bilattice . Similarly, having a bilattice we may consider the lattice . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples...
Y. A. Abramovich, A. K. Kitover (2003)
Studia Mathematica
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The following properties of C[0,1] are proved here. Let T: C[0,1] → Y be a disjointness preserving bijection onto an arbitrary vector lattice Y. Then the inverse operator is also disjointness preserving, the operator T is regular, and the vector lattice Y is order isomorphic to C[0,1]. In particular if Y is a normed lattice, then T is also automatically norm continuous. A major step needed for proving these properties is provided by Theorem 3.1 asserting that T satisfies some technical...
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 -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.