Results 271 to 280 of about 16,174 (299)
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International Journal of Mathematics, 2001
We study the operation E → cl (E) defined on subsets E of a unital ring R, where x ∈ cl (E) if (x + Rb) ∩ E ≠ ∅ for each b in R such that Rx + Rb = R. This operation, which strongly resembles a closure, originates in algebraic K-theory. For any left ideal L we show that cl (L) equals the intersection of the maximal left ideals of R containing L ...
Ara, P. +2 more
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We study the operation E → cl (E) defined on subsets E of a unital ring R, where x ∈ cl (E) if (x + Rb) ∩ E ≠ ∅ for each b in R such that Rx + Rb = R. This operation, which strongly resembles a closure, originates in algebraic K-theory. For any left ideal L we show that cl (L) equals the intersection of the maximal left ideals of R containing L ...
Ara, P. +2 more
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Applied Categorical Structures, 1994
In an \((E,{\mathcal M})\)-category \({\mathcal X}\) for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in \({\mathcal M}\) to factor through the ``lattice'' of all closure operators on \({\mathcal M}\), and to factor through certain sublattices. This leads to the
Gabriele Castellini +2 more
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In an \((E,{\mathcal M})\)-category \({\mathcal X}\) for sinks, we identify necessary conditions for Galois connections from the power collection of the class of (composable pairs) of morphisms in \({\mathcal M}\) to factor through the ``lattice'' of all closure operators on \({\mathcal M}\), and to factor through certain sublattices. This leads to the
Gabriele Castellini +2 more
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Closure Operators with Respect to a Functor
Applied Categorical Structures, 2001For a functor \(U:{\mathcal A}\to X\) into a category \({\mathcal X}\) with a factorization structure, the paper introduces a categorical notion of closure operator for subobjects in \({\mathcal X}\) of objects of type \(UA\). When applied in the case that \(U\) is the identity functor, it coincides with the notion introduced by \textit{D.
Gabriele Castellini, Eraldo Giuli
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2005
Program analysis commonly makes use of Boolean functions to express information about run-time states. Many important classes of Boolean functions used this way, such as the monotone functions and the Boolean Horn functions, have simple semantic characterisations.
Peter Schachte, Harald Søndergaard
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Program analysis commonly makes use of Boolean functions to express information about run-time states. Many important classes of Boolean functions used this way, such as the monotone functions and the Boolean Horn functions, have simple semantic characterisations.
Peter Schachte, Harald Søndergaard
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U-Closure Operators and Compactness
Applied Categorical Structures, 2005In this paper the authors introduce a notion of compactness in the following way: Let \({\mathcal A}\) be a category, \(\chi \) a finitely complete category with a proper \((\varepsilon ,{\mathcal M})\)-factorization structure for morphisms and \(U:{\mathcal A}\rightarrow \chi \) a functor. A pair \((A,m)\) with \(A\) object of \({\mathcal A}\) and \(m:
Gabriele Castellini, Eraldo Giuli
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TOPOLOGICAL CATEGORIES AND CLOSURE OPERATORS
Quaestiones Mathematicae, 1988Abstract It is shown that the category CS of closure spaces is a topological category. For each epireflective subcategory A of a topological category X a functor F A :X → X is defined and used to extend to the general case of topological categories some results given in [4], [5] and [10] for epireflective subcategories of the category Top of ...
Dikranjan D, Giuli E, TOZZI, Anna
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Openness with Respect to a Closure Operator
Applied Categorical Structures, 2000The abstract notion of a closure operator \(c\) introduced by \textit{E. Giuli} and \textit{D. Dikranyan} [Topology Appl. 27, 129-143 (1987; Zbl 0634.54008)] permits to define easily the notion of \(c\)-closed map (loc. cit.). The authors study \(c\)-open maps [introduced by \textit{W. Tholen} and \textit{D.
Eraldo Giuli, Walter Tholen
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Operations on Closure Operators
1995Despite the powerful continuity condition, the notion of closure operator is very general. It is therefore important to provide tools for improving a given operator. Fortunately, there is a natural lattice structure for closure operators that allows us to distinguish between properties stable under meet (idempotency, hereditariness, productivity), and ...
D. Dikranjan, W. Tholen
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Connectedness with Respect to a Closure Operator
Applied Categorical Structures, 2001For categories \(\mathcal C\) that are supplied with a factorization structure \(({\mathcal E}, M)\) for sinks, a closure operator \(C\) and a subclass \(N\) of \(M\), the author introduces a concept of connected objects. He demonstrates that under suitable additional conditions on \(\mathcal C\) many classical results about topological connectedness ...
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