Results 1 to 10 of about 507 (79)
Infratopological bornologies and Mackey convergence of series [PDF]
Publicacions Matemàtiques, 1986 In this paper some aspects of ínfratopological bornologies are discussed. First, it is shown that bornologies with countable basis are infratopological. Second, it is shown that the convergence of series presents some pathologies beyond this class.
Canela Campos, Miguel Ángel +1 more
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Uniformizable and realcompact bornological universes [PDF]
Applied General Topology, 2009 Bornological universes were introduced some time ago by Hu and obtained renewed interest in recent articles on convergence in hyperspaces and function spaces and optimization theory.
Tom Vroegrijk
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Some remarks about Mackey convergence
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper, we examine Mackey convergence with respect to K-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K- convergent
Józef Burzyk, Thomas E. Gilsdorf
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Bornological Completion of Locally Convex Cones [PDF]
Sahand Communications in Mathematical Analysis, 2020 In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion
Davood Ayaseh, Asghar Ranjbari
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Cardinal Functions, Bornologies and Strong Whitney convergence
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2022 17 ...
Chauhan, Tarun Kumar, Jindal, Varun
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Strong Whitney convergence on bornologies
Filomat, 2022 The strong Whitney convergence on bornology introduced by Caserta in [9] is a generalization of the strong uniform convergence on bornology introduced by Beer-Levi in [5]. This paper aims to study some important topological properties of the space of all real valued continuous functions on a metric space endowed with the topologies of ...
Tarun Chauhan, Varun Jindal
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Bornological Convergence and Shields
Mediterranean Journal of Mathematics, 2011 Starting with an ideal \(\mathcal{S}\), that is, a family \(\mathcal{S}\) of nonempty subsets of a metric space \(\langle X,d\rangle\) that is closed with respect to taking finite unions and taking nonempty subsets and considering the \(\epsilon\)-enlargement of a set \(E\subseteq X\) (for \(\epsilon>0\)), defined by \(E^\epsilon:=\bigcup_{a\in E}S_ ...
Beer, G: Costantini, C, LEVI, SANDRO
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Journal of Mathematical Analysis and Applications, 2004 The authors consider some special topologies of hyperspaces based on so-called bornologies. A bornology on a set \(X\) is a family \(\mathcal S\) of subsets of \(X\) such that: \(\mathcal S\) is a cover of \(X\), \(\mathcal S\) is closed under subsets and \(\mathcal S\) is closed under finite unions.
Lechicki, A, LEVI, SANDRO, Spakowski, A.
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The Alexandroff property and the preservation of strong uniform continuity
Applied General Topology, 2010 In this paper we extend the theory of strong uniform continuity and strong uniform convergence, developed in the setting of metric spaces in, to the uniform space setting, where again the notion of shields plays a key role.
Gerald Beer
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Filter bornological convergence in topological vector spaces
Filomat, 2021 The concept of ?-enlargement defined on metric spaces is generalized to the concept of Uenlargement by using neighborhoods U of the zero of the space on topological vector spaces. By using U-enlargement, we define the bornological convergence for nets of sets in topological vector spaces and we examine some of their properties.
Sümeyra Aydemir, Hüseyin Albayrak
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