Displaying similar documents to “On the lattice structure of T 1 topologies”

On the special context of independent sets

Vladimír Slezák (2001)

Discussiones Mathematicae - General Algebra and Applications

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In this paper the context of independent sets J L p 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.

The Banach lattice C[0,1] is super d-rigid

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 T - 1 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...

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 .

An extension method for t-norms on subintervals to t-norms on bounded lattices

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 L from the t-norm on a subinterval of L need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other...

Dieudonné-type theorems for lattice group-valued k -triangular set functions

Antonio Boccuto, Xenofon Dimitriou (2019)

Kybernetika

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Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for k -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.

Hyperreflexivity of bilattices

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 ℒ we can construct the bilattice Σ ℒ . Similarly, having a bilattice Σ we may consider the lattice ℒ Σ . In this paper we study the relationship between hyperreflexivity of subspace lattices and of their associated bilattices. Some examples...

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,...

On central atoms of Archimedean atomic lattice effect algebras

Martin Kalina (2010)

Kybernetika

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If element z of a lattice effect algebra ( E , ⊕ , 0 , 1 ) is central, then the interval [ 0 , z ] is a lattice effect algebra with the new top element z and with inherited partial binary operation ⊕ . It is a known fact that if the set C ( E ) of central elements of E is an atomic Boolean algebra and the supremum of all atoms of C ( E ) in E equals to the top element of E , then E is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether C ( E ) is...