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Journal articles on the topic 'Bornological convergences'

Author: Grafiati

Published: 10 March 2023

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1

Lechicki, A., S. Levi, and A. Spakowski. "Bornological convergences." Journal of Mathematical Analysis and Applications 297, no. 2 (September 2004): 751–70. http://dx.doi.org/10.1016/j.jmaa.2004.04.046.

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2

Rodríguez-López, Jesús, and M. A. Sánchez-Granero. "Some properties of bornological convergences." Topology and its Applications 158, no. 1 (January 2011): 101–17. http://dx.doi.org/10.1016/j.topol.2010.10.009.

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3

Di Concilio, A., and C. Guadagni. "Bornological convergences and local proximity spaces." Topology and its Applications 173 (August 2014): 294–307. http://dx.doi.org/10.1016/j.topol.2014.06.005.

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4

Rosa, Marco, and Paolo Vitolo. "Bornological Convergences on the Hyperspace of a Uniformizable Space." Set-Valued and Variational Analysis 24, no. 4 (January 9, 2016): 597–618. http://dx.doi.org/10.1007/s11228-015-0359-y.

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5

Jin, Zhen-yu, and Cong-hua Yan. "Induced L-bornological vector spaces and L-Mackey convergence1." Journal of Intelligent & Fuzzy Systems 40, no. 1 (January 4, 2021): 1277–85. http://dx.doi.org/10.3233/jifs-201599.

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Motivated by the concept of lattice-bornological vector spaces of J. Paseka, S. Solovyov and M. Stehlík, which extends bornological vector spaces to the fuzzy setting over a complete lattice, this paper continues to study the theory of L-bornological vector spaces. The specific description of L-bornological vector spaces is presented, some properties of Lowen functors between the category of bornological vector spaces and the category of L-bornological vector spaces are discussed. In addition, the notions and some properties of L-Mackey convergence and separation in L-bornological vector spaces are showed. The equivalent characterization of separation in L-bornological vector spaces in terms of L-Mackey convergence is obtained in particular.

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6

Aydemir, Sümeyra, and Hüseyin Albayrak. "Filter bornological convergence in topological vector spaces." Filomat 35, no. 11 (2021): 3733–43. http://dx.doi.org/10.2298/fil2111733a.

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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. By using filters defined on natural numbers, we define the concept of filter bornological convergence on sequences of sets, which is a more general concept than the bornological convergence defined on topological vector spaces. We give similar results for the filter bornological convergence.

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7

Burzyk, Józef, and Thomas E. Gilsdorf. "Some remarks about Mackey convergence." International Journal of Mathematics and Mathematical Sciences 18, no. 4 (1995): 659–64. http://dx.doi.org/10.1155/s0161171295000846.

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In this paper, we examine Mackey convergence with respect toK-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply propertyK; there are spaces havingK- convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence condition, is barrelled, but is not bornological; and if a space satisfies the biackey convergence condition and every sequentially continuous seminorm is continuous, then the space is bornological.

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8

Beer, Gerald, Camillo Costantini, and Sandro Lev. "Bornological Convergence and Shields." Mediterranean Journal of Mathematics 10, no. 1 (November 24, 2011): 529–60. http://dx.doi.org/10.1007/s00009-011-0162-4.

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9

Beer, Gerald, and Sandro Levi. "Gap, Excess and Bornological Convergence." Set-Valued Analysis 16, no. 4 (April 25, 2008): 489–506. http://dx.doi.org/10.1007/s11228-008-0086-8.

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10

Jin, Zhen-Yu, and Cong-Hua Yan. "Fuzzifying bornological linear spaces." Journal of Intelligent & Fuzzy Systems 42, no. 3 (February 2, 2022): 2347–58. http://dx.doi.org/10.3233/jifs-211644.

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In this paper, a notion of fuzzifying bornological linear spaces is introduced and the necessary and sufficient condition for fuzzifying bornologies to be compatible with linear structure is discussed. The characterizations of convergence and separation in fuzzifying bornological linear spaces are showed. In particular, some examples with respect to linear fuzzifying bornologies induced by probabilistic normed spaces and fuzzifying topological linear spaces are also provided.

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11

Ayaseh, Davood, and Asghar Ranjbari. "Bornological Convergence in Locally Convex Cones." Mediterranean Journal of Mathematics 13, no. 4 (May 27, 2015): 1921–31. http://dx.doi.org/10.1007/s00009-015-0578-3.

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12

Abdul-Hussein, Mushtaq Shaker, and G. S. Srivastava. "A study on bornological properties of the space of entire functions of several complex variables." Tamkang Journal of Mathematics 33, no. 4 (December 31, 2002): 289–302. http://dx.doi.org/10.5556/j.tkjm.33.2002.277.

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Spaces of entire functions of several complex variables occupy an important position in view of their vast applications in various branches of mathematics, for instance, the classical analysis, theory of approximation, theory of topological bases etc. With an idea of correlating entire functions with certain aspects in the theory of basis in locally convex spaces, we have investigated in this paper the bornological aspects of the space $X$ of integral functions of several complex variables. By $Y$ we denote the space of all power series with positive radius of convergence at the origin. We introduce bornologies on $X$ and $Y$ and prove that $Y$ is a convex bornological vector space which is the completion of the convex bornological vector space $X$.

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13

Katsaras, A. K., and V. Benekas. "Sequential Convergence in Topological Vector Spaces." gmj 2, no. 2 (April 1995): 151–64. http://dx.doi.org/10.1515/gmj.1995.151.

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Abstract For a given linear topology τ, on a vector space E, the finest linear topology having the same τ convergent sequences, and the finest linear topology on E having the same τ precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their properties are studied.

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14

Vroegrijk, Tom. "On the semi-uniformity of bornological convergence." Quaestiones Mathematicae 38, no. 2 (March 4, 2015): 285–96. http://dx.doi.org/10.2989/16073606.2014.981725.

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15

Das, Subhankar, and Debraj Chandra. "Certain observations on statistical variations of bornological covers." Filomat 35, no. 7 (2021): 2303–15. http://dx.doi.org/10.2298/fil2107303d.

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We primarily make a general approach to the study of open covers and related selection principles using the idea of statistical convergence in metric space. In the process we are able to extend some results in (Caserta et al. 2012; Chandra et al. 2020) where bornological covers and related selection principles in metric spaces have been investigated using the idea of strong uniform convergence (Beer and Levi, 2009) on a bornology. We introduce the notion of statistical-Bs-cover, statistically-strong-B-Hurewicz and statistically-strong-B-groupable cover and study some of its properties mainly related to the selection principles and corresponding games. Also some properties like statistically-strictly Fr?chet Urysohn, statistically-Reznichenko property and countable fan tightness have also been investigated in C(X) with respect to the topology of strong uniform convergence ?sB.

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16

Brooks, J. K., and J. T. Kozinski. "Stochastic Integration in Abstract Spaces." International Journal of Stochastic Analysis 2010 (August 16, 2010): 1–7. http://dx.doi.org/10.1155/2010/217372.

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We establish the existence of a stochastic integral in a nuclear space setting as follows. Let , , and be nuclear spaces which satisfy the following conditions: the spaces are reflexive, complete, bornological spaces such that their strong duals also satisfy these conditions. Assume that there is a continuous bilinear mapping of into . If is an integrable, -valued predictable process and is an -valued square integrable martingale, then there exists a -valued process called the stochastic integral. The Lebesgue space of these integrable processes is studied and convergence theorems are given. Extensions to general locally convex spaces are presented.

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17

Khadim, Sana, and Muhammad Qasim. "Quotient reflective subcategories of the category of bounded uniform filter spaces." AIMS Mathematics 7, no. 9 (2022): 16632–48. http://dx.doi.org/10.3934/math.2022911.

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<abstract><p>Previously, several notions of $ T_{0} $ and $ T_{1} $ objects have been studied and examined in various topological categories. In this paper, we characterize each of $ T_{0} $ and $ T_{1} $ objects in the categories of several types of bounded uniform filter spaces and examine their mutual relations, and compare that with the usual ones. Moreover, it is shown that under $ T_{0} $ (resp. $ T_{1} $) condition, the category of preuniform (resp. semiuniform) convergence spaces and the category of bornological (resp. symmetric) bounded uniform filter spaces are isomorphic. Finally, it is proved that the category of each of $ T_{0} $ (resp. $ T_{1} $) bounded uniform filter space are quotient reflective subcategories of the category of bounded uniform filter spaces.</p></abstract>

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18

Govaerts, W. "Duality properties of spaces of non-Archimedean valued functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 42, no. 1 (February 1987): 48–56. http://dx.doi.org/10.1017/s1446788700033942.

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AbstractLet C(X, F) be the space of all continuous functions from the ultraregular compact Hausdorff space X into the separated locally K-convex space F; K is a complete, but not necessarily spherically complete, non-Archimedean valued field and C(X, F) is provided with the topology of uniform convergence on X We prove that C(X, F) is K-barrelled (respectively K-quasibarrelled) if and only if F is K-barrelled (respectively K-quasibarrelled) This is not true in the case of R or C-valued functions. No complete characterization of the K-bornological space C(X, F) is obtained, but our results are, nevertheless, slightly better than the Archimedean ones. Finally, we introduce a notion of K-ultrabornological spaces for K non-spherically complete and use it to study K-ultrabornological spaces C(X, F).

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19

Bernardes Jr., Nilson, and Dinamérico Pombo Jr. "Mackey convergence and bornological topological modules." Rendiconti Lincei - Matematica e Applicazioni, 2010, 299–304. http://dx.doi.org/10.4171/rlm/574.

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