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Abstract  

Closure algebras have been intensively studied in literature ([2], [3], [11], ...) but, up to now, little interest has been devoted to subalgebras of closure algebras. In this paper, the methods of [16] are adapted to characterize closure algebras with a distributive, or a Boolean, subalgebra lattice.

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Abstract  

We define two closure operators of some well-known topological categories and investigate the relationships between these closure operators and the one that is given in [9]. As a consequence, we characterize separation properties T 0, T 1, and T 2 for these well-known categories and compare them with the ones that are given in [3] and [6]. Finally, we characterize the epimorphisms in the subcategories of these given categories.

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Abstract  

Notions of strongly and absolutely closed objects with respect to a closure operator X on an arbitrary category X and with respect to a subcategory Y are introduced. This yields two Galois connections between closure operators on a given category X and subclasses of X, whose fixed points are studied. A relationship with some compactness notions is shown and examples are provided.

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We consider the question of whether a compact space will always have a discrete subset whose closure has the same cardinality as the whole space. We obtain many positive results for compact spaces of countable tightness and a consistent negative result for a space of tightness and density ?1.

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. [2] A . Banerjee , K. K . Das , and S . Haque . Integral closure of powers of edge ideals of weighted oriented graphs . Preprint . [3] A . Banerjee , K. K . Das , and S . Selvaraja . Powers of edge ideals of weighted oriented graphs with

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Abstract  

We introduce and study a concept of neighborhoods with respect to a categorical closure operator. The concept, which is based on using pseudocomplements in subobject lattices, naturally generalizes the classical neighborhoods in topological spaces and we show that it behaves accordingly. We investigate also separation and compactness defined in a natural way by the help of the neighboorhoods introduced.

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Abstract  

Patents are important intellectual assets for companies to defend or to claim their technological rights. To control R&D cost, companies should carefully examine their patents by patent quality. Approaches to evaluating patent quality are mostly a posteriori uses of factual information of patent quality. This paper examined whether patent quality can be predicted a priori, i.e., during the early years after a patent is granted, by analyzing information embedded in a network of patent citations. Social network analysis was applied to analyze two network positions occupied by a patent, brokerage and closure to determine whether either position is a good predictor of patent quality. Patent renewal decisions and forward citations were adopted as surrogates of patent quality. The analytical results showed that forward citations can be positively predicted by the brokerage position and negatively predicted by the closure position in the early and mature stages. Renewal decisions can be negatively predicted by the brokerage position in the early stage, and the closure position influences the renewal decision in a different way in the early and mature stages. These analytical results imply that a company should focus on developing patents that bridge different technologies as its technological developments reach maturity.

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In this paper we study the semigroup ℐ (ℕ) of partial cofinal monotone bijective transformations of the set of positive integers ℕ. We show that the semigroup ℐ (ℕ) has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology τ on ℐ (ℕ) such that (ℐ (ℕ); τ) is a topological inverse semigroup, is discrete. Finally, we describe the closure of (ℐ (ℕ); τ) in a topological semigroup.

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Acta Mathematica Hungarica
Authors:
G. C. L. Brümmer
,
E. Giuli
, and
D. Holgate
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