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Relevant bibliographies by topics / Topological vector spaces

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Academic literature on the topic 'Topological vector spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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Journal articles on the topic "Topological vector spaces"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Topological vector spaces"

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Nielsen, Mark J. "Tilings of topological vector spaces /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5763.

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Vera, Mendoza Rigoberto. "Linear operations on locally convex topological vector spaces." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186699.

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Our purpose is to extend, to the class of linear operators on a locally convex space, some of the results of spectral theory. In order to do this we had to introduce some topologies on the space of operators that are not locally convex. These topologies are of interest in their own right, and have proved useful in enabling us to attain our goal. There is an important class of topological vector spaces named ab-spaces (almost bornological spaces), but there are not too many facts about them. We briefly discuss some new results and give a characterization of those spaces in Chapter 3.

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Pinchuck, Andrew. "Extension theorems on L-topological spaces and L-fuzzy vector spaces." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005219.

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A non-trivial example of an L-topological space, the fuzzy real line is examined. Various L-topological properties and their relationships are developed. Extension theorems on the L-fuzzy real line as well as extension theorems on more general L-topological spaces follow. Finally, a theory of L-fuzzy vector spaces leads up to a fuzzy version of the Hahn-Banach theorem.

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Lear, Jeffrey Charles. "Barrelled spaces." Instructions for remote access. Click here to access this electronic resource. Access available to Kutztown University faculty, staff, and students only, 1993. http://www.kutztown.edu/library/services/remote_access.asp.

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Thesis (M.A.)--Kutztown University of Pennsylvania, 1993.
Source: Masters Abstracts International, Volume: 45-06, page: 3171. Abstract precedes thesis title page as [2] preliminary leaves. Typescript. Includes bibliographical references (leaf 39).

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Griesan, Raymond William. "Nabla spaces, the theory of the locally convex topologies (2-norms, etc.) which arise from the mensuration of triangles." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184510.

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Metric topologies can be viewed as one-dimensional measures. This dissertation is a topological study of two-dimensional measures. Attention is focused on locally convex vector topologies on infinite dimensional real spaces. A nabla (referred to in the literature as a 2-norm) is the analogue of a norm which assigns areas to the parallelograms. Nablas are defined for the classical normed spaces and techniques are developed for defining nablas on arbitrary spaces. The work here brings out a strong connection with tensor and wedge products. Aside from the normable theory, it is shown that nabla topologies need not be metrizable or Mackey. A class of concretely given non-Mackey nablas on the ℓp and Lp spaces is introduced and extensively analyzed. Among other results it is found that the topological dual of ℓ₁ with respect to these nabla topologies is C₀, one of the spaces infamous for having no normed predual. Also, a connection is made with the theory of two-norm convergence (not to be confused with 2-norms). In addition to the hard analysis on the classical spaces, a duality framework from which to study the softer aspects is introduced. This theory is developed in analogy with polar duality. The ideas corresponding to barrelledness, quasi-barrelledness, equicontinuity and so on are developed. This dissertation concludes with a discussion of angles in arbitrary normed spaces and a list of open questions.

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Albuquerque, Nacib André Gurgel e. "Hardy-Littlewood/Bohnenblust-Hille multilinear inequalities and Peano curves on topological vector spaces." Universidade Federal da Paraíba, 2014. http://tede.biblioteca.ufpb.br:8080/handle/tede/7448.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work is divided in two subjects. The first concerns about the Bohnenblust-Hille and Hardy- Littlewood multilinear inequalities. We obtain optimal and definitive generalizations for both inequalities. Moreover, the approach presented provides much simpler and straightforward proofs than the previous one known, and we are able to show that in most cases the exponents involved are optimal. The technique used is a combination of probabilistic tools and of an interpolative approach; this former technique is also employed in this thesis to improve the constants for vector-valued Bohnenblust-Hille type inequalities. The second subject has as starting point the existence of Peano spaces, that is, Haurdor spaces that are continuous image of the unit interval. From the point of view of lineability we analyze the set of continuous surjections from an arbitrary euclidean spaces on topological spaces that are, in some natural sense, covered by Peano spaces, and we conclude that large algebras are found within the families studied. We provide several optimal and definitive result on euclidean spaces, and, moreover, an optimal lineability result on those special topological vector spaces.
Este trabalho édividido em dois temas. O primeiro diz respeito às desigualdades multilineares de Bohnenblust-Hille e Hardy-Littlewood. Obtemos generalizações ótimas e definitivas para ambas desigualdades. Mais ainda, a abordagem apresentada fornece demonstrações mais simples e diretas do que as conhecidas anteriormente, além de sermos capazes de mostrar que os expoentes envolvidos são ótimos em varias situações. A técnica utilizada combina ferramentas probabilísticas e interpolativas; esta ultima e ainda usada para melhorar as estimativas das versões vetoriais da desigualdade de Bohnenblust-Hille. O segundo tema possui como ponto de partida a existência de espaços de Peano, ou seja, os espaços de Hausdor que são imagem contínua do intervalo unitário. Sob o ponto de vista da lineabilidade, analisamos o conjunto das sobrejecoes contínuas de um espaço euclidiano arbitrário em um espaço topológico que, de certa forma, e coberto por espaços de Peano, e concluímos que grandes álgebras são encontradas nas famílias estudadas. Fornecemos vários resultados ótimos e definitivos em espaços euclidianos, e, mais ainda, um resultado de lineabilidade ótimo naqueles espaços vetoriais topológicos especiais.

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Toolan, Timothy M. "Advances in sliding window subspace tracking /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3206257.

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Costa, Debora Cristina Brandt. "Operadores hipercíclicos em espaços vetoriais topológicos." Universidade de São Paulo, 2007. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-01082007-115014/.

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Dado E um espaço vetorial topológico e T um operador linear contínuo em E, diremos que T é hipercíclico se, para algum elemento x pertencente a E, a órbita de x sob T, Orb(x,T)={x, Tx, T^2 x,...}, for densa em E. Nosso objetivo será apresentar alguns resultados sobre hiperciclicidade e observar como alguns espaços comportam-se diante dessa classe de operadores. \\\\
Let E be a topological vector space and T a continuous linear operator on E. We say that T is hypercyclic if, for some x in E, the orbit of x on T, Orb(x,T)={x, Tx, T^2 x,...}, is dense in E. Our aim will be to study some results about hypercyclicity and to observe how some spaces behave regarding this class of operators.

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Cavalcante, Wasthenny Vasconcelos. "Espaços Vetoriais Topológicos." Universidade Federal da Paraíba, 2015. http://tede.biblioteca.ufpb.br:8080/handle/tede/9277.

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In this work we investigate the concept of topological vector spaces and their properties. In the rst chapter we present two sections of basic results and in the other sections we present a more general study of such spaces. In the second chapter we restrict ourselves to the real scalar eld and we study, in the context of locally convex spaces, the Hahn-Banach and Banach-Alaoglu theorems. We also build the weak, weak-star, of bounded convergence and of pointwise convergence topologies. Finally we investigate the Theorem of Banach-Steinhauss, the Open Mapping Theorem and the Closed Graph Theorem.
Neste trabalho, estudamos o conceito de espa cos vetoriais topol ogicos e suas propriedades. No primeiro cap tulo, apresentamos duas se c~oes de resultados b asicos e, nas demais se c~oes, apresentamos um estudo sobre tais espa cos de forma mais ampla. No segundo cap tulo, restringimo-nos ao corpo dos reais e fazemos um estudo sobre os espa cos localmente convexos, o Teorema de Hahn-Banach, o Teorema de Banach- Alaoglu, constru mos as topologias fraca, fraca-estrela, da converg^encia limitada e da converg^encia pontual. Por ultimo, estudamos o Teorema da Limita c~ao Uniforme, o Teorema do Gr a co Fechado e o da Aplica c~ao Aberta no contexto mais geral dos espa cos de Fr echet.

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Karliczek, Martin. "Elements of conditional optimization and their applications to order theory." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2014. http://dx.doi.org/10.18452/17085.

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In dieser Arbeit beweisen wir für Optimierungsprobleme in L0-Moduln relevante Resultate und untersuchen Anwendungen für die Darstellung von Präferenzen. Im ersten Kapitel geht es um quasikonkave, monotone und lokale Funktionen von einem L0-Modul X nach L0, die wir robust darstellen. Im zweiten Kapitel entwickeln wir das Ekeland’sche Variationsprinzip für L0-Moduln, die eine L0-Metrik besitzen. Wir beweisen eine L0 -Variante einer Verallgemeinerung des Ekeland’schen Theorems. Der Beweis des Brouwerschen Fixpunktsatzes für Funktionen, die auf (L0)^d definiert sind, wird in Kapitel 3 behandelt. Wir definieren das Konzept des Simplexes in (L0)^d und beweisen, dass jede lokale, folgenstetige Funktion darauf einen Fixpunkt besitzt. Dies nutzen wir, um den Fixpunktsatz auch für Funktionen auf beliebigen abgeschlossenen, L0 -konvexen Mengen zu zeigen. Eine allgemeinere Struktur als L0 ist die bedingte Menge. Im vierten Kapitel behandeln wir bedingte topologische Vektorräume. Wir führen das Konzept der Dualität für bedingte Mengen ein und beweisen Theoreme der Funktionalanalysis darauf, unter anderem das Theorem von Banach-Alaoglu und Krein-Šmulian. Im fünften Kapitel widmen wir uns der Darstellung mit wandernden konvexen Mengen. Wir zeigen danach, wie die Transitivität für diese Darstellungsform beschrieben werden kann. Abschließend modellieren wir die Eigenschaft, dass die Transitivität einer Relation nur für ähnliche Elemente gesichert ist und diskutieren Arten der Darstellung solcher Relationen.
In this thesis, we prove results relevant for optimization problems in L0-modules and study applications to order theory. The first part deals with the notion of an Assessment Index (AI). For an L0 -module X an AI is a quasiconcave, monotone and local function mapping to L0. We prove a robust representation of these AIs. In the second chapter of this thesis, we develop Ekeland’s variational principle for L0-modules allowing for an L0-metric. We prove an L0-Version of a generalization of Ekeland’s theorem. A further application of L0 -theory is examined in the third chapter of this thesis, namely an extension of the Brouwer fixed point theorem to functions on (L0)^d . We define a conditional simplex, which is a simplex with respect to L0 , and prove that every local, sequentially continuous function has a fixed point. We extend the fixed point theorem to arbitrary closed, L0-convex sets. A more general structure than L0 -modules is the concept of conditional sets. In the fourth chapter of the thesis, we study conditional topological vector spaces. We examine the concept of duality for conditional sets and prove results of functional analysis: among others, the Banach-Alaoglu and the Krein-Šmulian theorem. Any L0 -module being a conditional set allows to apply all results to L0 -theory. In the fifth chapter, we discuss the property of transitivity of relations and its connection to certain forms of representations. After a survey of common representations of preferences, we attend to relations induced by moving convex sets which are relations of the form that x is preferred to y if and only if x − y is in a convex set depending on y. We examine in which cases such a representation is transitive. Finally, we exhibit nontransitivity due to dissimilarity of the compared object and discuss representations for relations of that type.

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Books on the topic "Topological vector spaces"

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1940-, Beckenstein Edward, ed. Topological vector spaces. 2nd ed. Boca Raton: Taylor & Francis, 2011.

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Schaefer, H. H., and M. P. Wolff. Topological Vector Spaces. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7.

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Bourbaki, Nicolas. Topological Vector Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-61715-7.

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Narici, Lawrence. Topological vector spaces. 2nd ed. Boca Raton, FL: CRC Press, 2011.

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Schaefer, Helmut H. Topological vector spaces. 2nd ed. New York: Springer, 1999.

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1940-, Beckenstein Edward, ed. Topological vector spaces. New York: M. Dekker, 1985.

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Nicolas Bourbaki. Topological vector spaces. Berlin: Springer-Verlag, 1987.

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Schaefer, H. H. Topological Vector Spaces. New York, NY: Springer New York, 1999.

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Topological vector spaces and distributions. Mineola, N.Y: Dover Publications, 2012.

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Horváth, John. Topological vector spaces and distributions. Mineola, N.Y: Dover Publications, 2012.

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Book chapters on the topic "Topological vector spaces"

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Schaefer, H. H., and M. P. Wolff. "Topological Vector Spaces." In Topological Vector Spaces, 12–35. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_2.

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Bourbaki, Nicolas. "Topological vector spaces over a valued division ring." In Topological Vector Spaces, 1–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_1.

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Bourbaki, Nicolas. "Convex sets and locally convex spaces." In Topological Vector Spaces, 31–125. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_2.

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Bourbaki, Nicolas. "Spaces of continuous linear mappings." In Topological Vector Spaces, 127–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_3.

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Bourbaki, Nicolas. "Duality in topological vector spaces." In Topological Vector Spaces, 177–252. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_4.

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Bourbaki, Nicolas. "Hilbertian spaces (elementary theory)." In Topological Vector Spaces, 253–331. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_5.

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Schaefer, H. H., and M. P. Wolff. "Prerequisites." In Topological Vector Spaces, 1–11. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_1.

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Schaefer, H. H., and M. P. Wolff. "Locally Convex Topological Vector Spaces." In Topological Vector Spaces, 36–72. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_3.

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Schaefer, H. H., and M. P. Wolff. "Linear Mappings." In Topological Vector Spaces, 73–121. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_4.

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Schaefer, H. H., and M. P. Wolff. "Duality." In Topological Vector Spaces, 122–202. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_5.

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Conference papers on the topic "Topological vector spaces"

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Latif, Raja Mohammad. "Almost Alpha – Topological Vector Spaces." In 2020 International Conference on Mathematics and Computers in Science and Engineering (MACISE). IEEE, 2020. http://dx.doi.org/10.1109/macise49704.2020.00019.

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Hussein, Jalal Hatem, and Talal Ali Al-Hawary. "On δ-topological vector spaces." In INTERNATIONAL CONFERENCE OF COMPUTATIONAL METHODS IN SCIENCES AND ENGINEERING ICCMSE 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0116708.

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Wu, Zhiyong. "Vector Equilibrium Problem in Topological Vector Spaces." In 2018 6th International Conference on Machinery, Materials and Computing Technology (ICMMCT 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/icmmct-18.2018.8.

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Zhang, Hua-Peng. "Generalized local boundedness of induced I(L)-topological vector spaces." In 2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2015. http://dx.doi.org/10.1109/fskd.2015.7381916.

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Kraus, Eugene J., Henk J. A. M. Heijmans, and Edward R. Dougherty. "Spatial-scaling-compatible morphological granulometries on locally convex topological vector spaces." In San Diego '92, edited by Paul D. Gader, Edward R. Dougherty, and Jean C. Serra. SPIE, 1992. http://dx.doi.org/10.1117/12.60649.

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Abbas, Ruaa K., and Boushra Y. Hussein. "A new kind of topological vector space: Topological approach vector space." In 3RD INTERNATIONAL SCIENTIFIC CONFERENCE OF ALKAFEEL UNIVERSITY (ISCKU 2021). AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0066971.

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Bao, Yuanlu, Zhenan Liu, and Jin Qu. "An effective topological adjustment on vector maps for AVL." In International Conference on Space information Technology, edited by Cheng Wang, Shan Zhong, and Xiulin Hu. SPIE, 2005. http://dx.doi.org/10.1117/12.657414.

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Gu, Guomin, and Weihong Wang. "Improved Vector Route Algorithm Bases on Raster Topological Space Model." In TENCON 2005 - 2005 IEEE Region 10 Conference. IEEE, 2005. http://dx.doi.org/10.1109/tencon.2005.301072.

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Kong, Yuqi, Fanchao Meng, and Ben Carterette. "A Topological Method for Comparing Document Semantics." In 9th International Conference on Natural Language Processing (NLP 2020). AIRCC Publishing Corporation, 2020. http://dx.doi.org/10.5121/csit.2020.101411.

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Comparing document semantics is one of the toughest tasks in both Natural Language Processing and Information Retrieval. To date, on one hand, the tools for this task are still rare. On the other hand, most relevant methods are devised from the statistic or the vector space model perspectives but nearly none from a topological perspective. In this paper, we hope to make a different sound. A novel algorithm based on topological persistence for comparing semantics similarity between two documents is proposed. Our experiments are conducted on a document dataset with human judges’ results. A collection of state-of-the-art methods are selected for comparison. The experimental results show that our algorithm can produce highly human-consistent results, and also beats most state-of-the-art methods though ties with NLTK.

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Hobbs, Linn W. "What Can Topological Models Tell Us About Glass Structure and Properties?" In Bragg Gratings, Photosensitivity, and Poling in Glass Fibers and Waveguides. Washington, D.C.: Optica Publishing Group, 1997. http://dx.doi.org/10.1364/bgppf.1997.jsua.2.

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Atomic arrangements in condensed matter partition three-dimensional space into polyhedra whose edges are interatomic vectors. These polyhedra, formally known as void polytopes, fill (tesselate) space, and their identity and arrangement can provide one description of a given atomic arrangement (Figure 1a) [1]. Other tessellations associated with space-filling of random structures are Voronoi polyhedral cells [2] and their dual the Delauney network [3]. These tessellations are relatively intuitive in two dimensions, but considerably more complex in three-dimensions—for example in tetrahedral networks like SiO2—where a set of as many as 126 void polyhedra may be required to model interstitial space [1]. Because many arrangements favor particular coordination of one atom by others, owing to bond orbital, radius ratio, or local electrostatic neutrality considerations, discrete coordination polyhedra comprise a subset of the possible void polytopes, and the structure may be described by the way in which coordination polyhedra are connected together and fill space by defining the remaining void polytopes. Space filling by connected structural units was a favorite description tool of early crystal chemists [4], and in fact the connectivity of such structural polytopes (number of polytopes sharing vertices, edges and faces) has been shown to correlate with glass-forming ability and extendability of aperiodic networks [5] and to govern the amorphizability of crystalline solids [6].

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Reports on the topic "Topological vector spaces"

1

Al Shumrani, Mohammed A. Partially Topological Vector Spaces. "Prof. Marin Drinov" Publishing House of Bulgarian Academy of Sciences, February 2019. http://dx.doi.org/10.7546/crabs.2019.02.01.

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