Every lattice is embeddable in the lattice of -topologies
Richard Valent (1973)
Colloquium Mathematicae
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Richard Valent (1973)
Colloquium Mathematicae
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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.
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 compact elements. We show that every algebraic lattice with at most compact elements is a complete sublattice of Cl(X).
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...
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 .
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...
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,...
Martin Kalina (2010)
Kybernetika
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If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether is...
Gábor Czédli (2009)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Let be a -ary lattice term. A -pointed lattice , will be called a -lattice (or a test lattice if is not specified), if is generated by and, in addition, for any -ary lattice term satisfying , in , the lattice identity holds in all lattices. In an elementary visual way, we construct a finite -lattice for each . If is a canonical lattice term, then coincides with the optimal -lattice of Freese, Ježek and Nation [Freese,...