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Journal articles on the topic 'Topological vector spaces'

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Published: 4 June 2021
Last updated: 6 September 2023

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1

Rajesh, N., and V. Vijayabharathi. "On strongly preirresolute topological vector spaces." Mathematica Bohemica 138, no. 1 (2013): 37–42. http://dx.doi.org/10.21136/mb.2013.143228.

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2

Chiney, Moumita, and S. K. Samanta. "IF topological vector spaces." Notes on Intuitionistic Fuzzy Sets 24, no. 2 (May 2018): 33–51. http://dx.doi.org/10.7546/nifs.2018.24.2.33-51.

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3

Ibrahim, Hariwan. "α-Topological Vector Spaces." Science Journal of University of Zakho 5, no. 1 (March 30, 2017): 107–11. http://dx.doi.org/10.25271/2017.5.1.310.

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4

Gabriyelyan, Saak S., and Sidney A. Morris. "Free topological vector spaces." Topology and its Applications 223 (June 2017): 30–49. http://dx.doi.org/10.1016/j.topol.2017.03.006.

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5

Khurana, Surjit Singh. "Order convergence of vector measures on topological spaces." Mathematica Bohemica 133, no. 1 (2008): 19–27. http://dx.doi.org/10.21136/mb.2008.133944.

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6

Muller, M. A. "Bornologiese pseudotopologiese vektorruimtes." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 9, no. 1 (July 5, 1990): 15–18. http://dx.doi.org/10.4102/satnt.v9i1.434.

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Homological spaces were defined by Hogbe-Nlend in 1971 and pseudo-topological spaces by Fischer in 1959. In this paper properties of bornological pseudo-topological vector spaces are investigated. A characterization of such spaces is obtained and it is shown that quotient spaces and direct sums o f boruological pseudo-topological vector spaces are bornological. Every bornological locally convex pseudo-topological vector space is shown to be the inductive limit in the category of pseudo-topological vector spaces of a family of locally convex topological vector spaces.
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7

Yan, Cong-Hua, and Cong-Xin Wu. "L-fuzzifying topological vector spaces." International Journal of Mathematics and Mathematical Sciences 2005, no. 13 (2005): 2081–93. http://dx.doi.org/10.1155/ijmms.2005.2081.

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The main purpose of this paper is to introduce a concept ofL-fuzzifying topological vector spaces (hereLis a completely distributive lattice) and study some of their basic properties. Also, a characterization of such spaces in terms of the correspondingL-fuzzifying neighborhood structure of the zero element is given. Finally, the conclusion that the category ofL-fuzzifying topological vector spaces is topological over the category of vector spaces is proved.
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8

Abbas, Fadhil, and Hassan A. Alhayo. "Fuzzy ideal topological vector spaces." Mathematica Slovaca 72, no. 4 (August 1, 2021): 993–1000. http://dx.doi.org/10.1515/ms-2022-0069.

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Abstract In this paper, we introduce the concept of fuzzy ideal topological vector spaces and study the basic properties of fuzzy-I-open and fuzzy-I-closed sets in fuzzy ideal topological vector spaces. Also, we study the properties of fuzzy-I-Hausdorff and fuzzy-I-compact in fuzzy ideal topological vector spaces. Furthermore, we introduce the concepts of fuzzy-I-homogenous space, fuzzy-I-monomorphism space, fuzzy-I-isomorphism space and fuzzy-I-automorphism space. Finally, we introduce the concepts of fuzzy-I-bounded set, fuzzy-I-balanced set, fuzzy-I-symmetric set and study their properties in fuzzy ideal topological vector spaces.
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9

Yan, Cong-hua, and Jin-xuan Fang. "I(L)-topological vector spaces and its level topological spaces." Fuzzy Sets and Systems 149, no. 3 (February 2005): 485–92. http://dx.doi.org/10.1016/j.fss.2004.01.006.

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10

Khan, Moizud Din, and Muhammad Asad Iqbal. "On Irresolute Topological Vector Spaces." Advances in Pure Mathematics 06, no. 02 (2016): 105–12. http://dx.doi.org/10.4236/apm.2016.62009.

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11

Khurana, Surjit Singh. "Vector Measures on Topological Spaces." gmj 14, no. 4 (December 2007): 687–98. http://dx.doi.org/10.1515/gmj.2007.687.

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Abstract Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀 τ (𝑋,𝐸), 𝑀 σ (𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.
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12

Buckley, J. J., and Aimin Yan. "Fuzzy topological vector spaces over." Fuzzy Sets and Systems 105, no. 2 (July 1999): 259–75. http://dx.doi.org/10.1016/s0165-0114(98)00325-x.

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13

Ka̧kol, J., and M. López-Pellicer. "On realcompact topological vector spaces." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 105, no. 1 (February 3, 2011): 39–70. http://dx.doi.org/10.1007/s13398-011-0003-0.

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14

Alzubaidi, S., and R. Khalil. "Remotality in topological vector spaces." International Mathematical Forum 12 (2017): 71–75. http://dx.doi.org/10.12988/imf.2017.611144.

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15

Lyudkovskiî, S. V. "k-Normed topological vector spaces." Siberian Mathematical Journal 41, no. 1 (January 2000): 141–54. http://dx.doi.org/10.1007/bf02674004.

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16

Gartside, P. M. "Nonstratifiability of topological vector spaces." Topology and its Applications 86, no. 2 (July 1998): 133–40. http://dx.doi.org/10.1016/s0166-8641(97)00113-2.

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17

Zhang, Hua-Peng, and Jin-Xuan Fang. "On -topological vector spaces generated by a co-tower of L-topological vector spaces." Fuzzy Sets and Systems 160, no. 20 (October 2009): 2926–36. http://dx.doi.org/10.1016/j.fss.2009.02.020.

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18

Ram, Madhu, Shallu Sharma, Sahil Billawria, and Amjad Hussain. "On almost \(s-\)topological vector spaces." Journal of Advanced Studies in Topology 9, no. 2 (December 21, 2018): 139–46. http://dx.doi.org/10.20454/jast.2018.1490.

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In this paper, we introduce the notion of almost \(s-\)topological vector spaces and present some examples and counterexamples of almost \(s-\)topological vector spaces. Some general properties of almost \(s-\)topological vector spaces are investigated.
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19

Yılmaz, Yılmaz, Sümeyye Çakan, and Şahika Aytekin. "Topological Quasilinear Spaces." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/951374.

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We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.
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20

Muller, M. A. "Newel-pseudotopologiese vektorruimtes." Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie 18, no. 3 (July 12, 1999): 89–93. http://dx.doi.org/10.4102/satnt.v18i3.726.

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Pseudo-topological spaces (i.e. limit spaces) were defined by Fischer in 1959. In this paper the theory of fuzzy pseudo-topological spaces is applied to vector spaces. We introduce the concept of boundedness in fuzzy pseudo-topological vector spaces.
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21

Krishna, S. V., and K. K. M. Sarma. "Fuzzy topological vector spaces — topological generation and normability." Fuzzy Sets and Systems 41, no. 1 (May 1991): 89–99. http://dx.doi.org/10.1016/0165-0114(91)90159-n.

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22

Latif, Raja Mohammad. "M – STAR – Irresolute Topological Vector Spaces." International Journal of Pure Mathematics 7 (February 8, 2021): 20–36. http://dx.doi.org/10.46300/91019.2020.7.4.

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In 2016 A. Devika and A. Thilagavathi introduced a new class of sets called M*-open sets and investigated some properties of these sets in topological spaces. In this paper, we introduce and study a new class of spaces, namely M*-irresolute topological vector spaces via M*-open sets. We explore and investigate several properties and characterizations of this new notion of M*-irresolute topological vector space. We give several characterizations of M*-Hausdorff space. Moreover, we show that the extreme point of the convex subset of M*-irresolute topological vector space X lies on the boundary.
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23

LEIDERMAN, ARKADY, and SIDNEY A. MORRIS. "EMBEDDINGS OF FREE TOPOLOGICAL VECTOR SPACES." Bulletin of the Australian Mathematical Society 101, no. 2 (August 20, 2019): 311–24. http://dx.doi.org/10.1017/s000497271900090x.

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It is proved that the free topological vector space $\mathbb{V}([0,1])$ contains an isomorphic copy of the free topological vector space $\mathbb{V}([0,1]^{n})$ for every finite-dimensional cube $[0,1]^{n}$, thereby answering an open question in the literature. We show that this result cannot be extended from the closed unit interval $[0,1]$ to general metrisable spaces. Indeed, we prove that the free topological vector space $\mathbb{V}(X)$ does not even have a vector subspace isomorphic as a topological vector space to $\mathbb{V}(X\oplus X)$, where $X$ is a Cook continuum, which is a one-dimensional compact metric space. This is also shown to be the case for a rigid Bernstein set, which is a zero-dimensional subspace of the real line.
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24

Robdera, Mangatiana A. "Compactness Principles for Topological Vector Spaces." Topological Algebra and its Applications 10, no. 1 (January 1, 2022): 246–54. http://dx.doi.org/10.1515/taa-2022-0131.

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Abstract We show that the many of the canonical quantifications of interrelated concepts, centered around compactness in the setting of metric spaces, can be easily generalized to the setting of topological linear spaces. Among other things, we obtain a generalization of the Hausdorff Total Boundedness Principle, of the Grothendieck Compactness Principle, as well as of the Convex Compactness Principle for topological vector spaces.
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25

Murali, V. "*—Inductive limits and partition of unity." International Journal of Mathematics and Mathematical Sciences 12, no. 3 (1989): 429–34. http://dx.doi.org/10.1155/s0161171289000529.

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In this note we define and discuss some properties of partition of unity on *-inductive limits of topological vector spaces. We prove that if a partition of unity exists on a *-inductive limit space of a collection of topological vector spaces, then it is isomorphic and homeomorphic to a subspace of a *-direct sum of topological vector spaces.
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26

Sharma, Shallu, Sahil Billawria, Madhu Ram, and Tsering Landol. "On Almost β-Topological Vector Spaces." OALib 06, no. 05 (2019): 1–9. http://dx.doi.org/10.4236/oalib.1105408.

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27

Valdivia, Manuel. "Products of Baire topological vector spaces." Fundamenta Mathematicae 125, no. 1 (1985): 71–80. http://dx.doi.org/10.4064/fm-125-1-71-80.

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28

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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29

Iro, Ain, and Leiki Loone. "Knopp’s core in topological vector spaces." Acta et Commentationes Universitatis Tartuensis de Mathematica 2 (December 31, 1998): 75–79. http://dx.doi.org/10.12697/acutm.1998.02.11.

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30

Harbi, Intesar, and Z. D. Al-Nafie. "Metrizability of Pseudo Topological Vector Spaces." Journal of Physics: Conference Series 1897, no. 1 (May 1, 2021): 012037. http://dx.doi.org/10.1088/1742-6596/1897/1/012037.

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31

Sharma, Shallu, Sahil Billawria, and Tsering Landol. "On Almost $\alpha$-Topological Vector Spaces." Missouri Journal of Mathematical Sciences 32, no. 1 (May 2020): 80–87. http://dx.doi.org/10.35834/2020/3201080.

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32

Shkarin, Stanislav. "Hypercyclic operators on topological vector spaces." Journal of the London Mathematical Society 86, no. 1 (March 19, 2012): 195–213. http://dx.doi.org/10.1112/jlms/jdr082.

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33

Yilmaz, Yilmaz. "Function bases for topological vector spaces." Topological Methods in Nonlinear Analysis 33, no. 2 (June 1, 2009): 335. http://dx.doi.org/10.12775/tmna.2009.023.

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34

Albuquerque, N., L. Bernal-González, D. Pellegrino, and J. B. Seoane-Sepúlveda. "Peano curves on topological vector spaces." Linear Algebra and its Applications 460 (November 2014): 81–96. http://dx.doi.org/10.1016/j.laa.2014.07.029.

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35

Li, Ronglu, Shin Min Kang, and C. Swartz. "Operator matrices on topological vector spaces." Journal of Mathematical Analysis and Applications 274, no. 2 (October 2002): 645–58. http://dx.doi.org/10.1016/s0022-247x(02)00322-0.

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36

Bakier, M. Y., and K. El-Saady. "Fuzzy topological ordered vector spaces I." Fuzzy Sets and Systems 54, no. 2 (March 1993): 213–20. http://dx.doi.org/10.1016/0165-0114(93)90278-p.

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37

Yan, C. "Locally bounded L-topological vector spaces." Information Sciences 159, no. 3-4 (February 15, 2004): 273–81. http://dx.doi.org/10.1016/j.ins.2003.07.016.

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38

Burke, Maxim R., and Stevo Todorcevic. "Bounded sets in topological vector spaces." Mathematische Annalen 305, no. 1 (May 1996): 103–25. http://dx.doi.org/10.1007/bf01444213.

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39

Lin, Fucai, and Chuan Liu. "Notes on free topological vector spaces." Topology and its Applications 281 (August 2020): 107191. http://dx.doi.org/10.1016/j.topol.2020.107191.

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40

Kye, Seung-Hyeok. "Several reflexivities in topological vector spaces." Journal of Mathematical Analysis and Applications 139, no. 2 (May 1989): 477–82. http://dx.doi.org/10.1016/0022-247x(89)90122-4.

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41

Katsaras, A. K., and V. Benekas. "Sequential convergence in topological vector spaces." Georgian Mathematical Journal 2, no. 2 (March 1995): 151–64. http://dx.doi.org/10.1007/bf02257476.

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42

Zhu, Jiang, George Isac, and Dun Zhao. "Pareto optimization in topological vector spaces." Journal of Mathematical Analysis and Applications 301, no. 1 (January 2005): 22–31. http://dx.doi.org/10.1016/j.jmaa.2004.07.003.

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43

Ferrer, J. R., I. Morales, and L. M. Sánchez Ruiz. "Sequential convergence in topological vector spaces." Topology and its Applications 108, no. 1 (November 2000): 1–6. http://dx.doi.org/10.1016/s0166-8641(99)00121-2.

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44

Glöckner, Helge. "Aspects of Differential Calculus Related to Infinite-Dimensional Vector Bundles and Poisson Vector Spaces." Axioms 11, no. 5 (May 9, 2022): 221. http://dx.doi.org/10.3390/axioms11050221.

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We prove various results in infinite-dimensional differential calculus that relate the differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: (1) in the theory of infinite-dimensional vector bundles, to construct new bundles from given ones, such as dual bundles, topological tensor products, infinite direct sums, and completions (under suitable hypotheses); (2) in the theory of locally convex Poisson vector spaces, to prove continuity of the Poisson bracket and continuity of passage from a function to the associated Hamiltonian vector field. Topological properties of topological vector spaces are essential for the studies, which allow the hypocontinuity of bilinear mappings to be exploited. Notably, we encounter kR-spaces and locally convex spaces E such that E×E is a kR-space.
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45

Zabeti. "Topological Algebras of Bounded Operators on Topological Vector Spaces." Journal of Advanced Research in Pure Mathematics 3, no. 1 (January 1, 2011): 22–26. http://dx.doi.org/10.5373/jarpm.438.052210.

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46

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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47

KOZLOWSKI, WOJCIECH M. "ON MODULATED TOPOLOGICAL VECTOR SPACES AND APPLICATIONS." Bulletin of the Australian Mathematical Society 101, no. 2 (July 10, 2019): 325–32. http://dx.doi.org/10.1017/s0004972719000716.

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We introduce a notion of modulated topological vector spaces, that generalises, among others, Banach and modular function spaces. As applications, we prove some results which extend Kirk’s and Browder’s fixed point theorems. The theory of modulated topological vector spaces provides a very minimalist framework, where powerful fixed point theorems are valid under a bare minimum of assumptions.
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48

AYDIN, ABDULLAH, and MUHAMMED ÇINAR. "StatisticalLY τ-Bounded Operators on Ordered Topological Vector Spaces." Journal of Science and Arts 22, no. 4 (December 30, 2022): 803–10. http://dx.doi.org/10.46939/j.sci.arts-22.4-a02.

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In this paper, we introduce statistical bounded sets on topological vector space. Also, we give the three notions of bounded operators from topological vector spaces to ordered topological vector spaces. Moreover, we show some relations between these operators and order bounded operators. Also, we give some algebraic properties of these operators with respect to the uniform convergence topology.
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49

Khan, Suhel A. "Generalized vector complementarity-type problems in topological vector spaces." Computers & Mathematics with Applications 59, no. 11 (June 2010): 3595–602. http://dx.doi.org/10.1016/j.camwa.2010.03.055.

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50

Ka̧kol, Jerzy, Arkady G. Leiderman, and Sidney A. Morris. "Nonseparable closed vector subspaces of separable topological vector spaces." Monatshefte für Mathematik 182, no. 1 (January 16, 2016): 39–47. http://dx.doi.org/10.1007/s00605-016-0876-2.

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