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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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...
Lifeng Li, Jianke Zhang, Chang Zhou (2019)
Kybernetika
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For a t-norm T on a bounded lattice , a partial order was recently defined and studied. In [11], it was pointed out that the binary relation is a partial order on , but may not be a lattice in general. In this paper, several sufficient conditions under which is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on such that is a lattice are presented.
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.
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...
Gül Deniz Çaylı (2019)
Kybernetika
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In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice based on a priori given t-norm acting on and t-conorm acting on for an arbitrary element . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice. ...
Gábor Czédli (2024)
Mathematica Bohemica
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Following G. Grätzer and E. Knapp (2007), a slim planar semimodular lattice, SPS lattice for short, is a finite planar semimodular lattice having no as a sublattice. An SPS lattice is a slim rectangular lattice if it has exactly two doubly irreducible elements and these two elements are complements of each other. A finite poset is said to be JConSPS-representable if there is an SPS lattice such that is isomorphic to the poset of join-irreducible congruences of . We prove that...
Ivan Chajda, Helmut Länger (2022)
Mathematica Bohemica
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We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular....
Lin Yang, Sheng-Liang Yang, Tian-Xiao He (2020)
Czechoslovak Mathematical Journal
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We introduce a new family of generalized Schröder matrices from the Riordan arrays which are obtained by counting of the weighted lattice paths with steps , , , and and not going above the line . We also consider the half of the generalized Delannoy matrix which is derived from the enumeration of these lattice paths with no restrictions. Correlations between these matrices are considered. By way of illustration, we give several examples of Riordan arrays of combinatorial interest....
S. Okada, W. J. Ricker, E. A. Sánchez Pérez
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The spaces L¹(m) of all m-integrable (resp. of all scalarly m-integrable) functions for a vector measure m, taking values in a complex locally convex Hausdorff space X (briefly, lcHs), are themselves lcHs for the mean convergence topology. Additionally, is always a complex vector lattice; this is not necessarily so for L¹(m). To identify precisely when L¹(m) is also a complex vector lattice is one of our central aims. Whenever X is sequentially complete, then this is the case. If,...
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...
Zbigniew Lipecki (2023)
Commentationes Mathematicae Universitatis Carolinae
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Let be a Banach lattice, and denote by its positive cone. The weak topology on is metrizable if and only if it coincides with the strong topology if and only if is Banach-lattice isomorphic to for a set . The weak topology on is metrizable if and only if is Banach-lattice isomorphic to a -space, where is a metrizable compact space.
Rafał Kapica (2003)
Colloquium Mathematicae
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Given a probability space (Ω,, P) and a closed subset X of a Banach lattice, we consider functions f: X × Ω → X and their iterates defined by f¹(x,ω) = f(x,ω₁), , and obtain theorems on the convergence (a.s. and in L¹) of the sequence (fⁿ(x,·)).