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Journal articles on the topic 'Duality spaces'

Author: Grafiati

Published: 4 June 2025

Last updated: 1 August 2025

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1

Aksnes, Edvard. "Tropical Poincaré duality spaces." Advances in Geometry 23, no. 3 (2023): 345–70. http://dx.doi.org/10.1515/advgeom-2023-0017.

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Abstract The tropical fundamental class of a rational balanced polyhedral fan induces cap products between tropical cohomology and tropical Borel–Moore homology. When all these cap products are isomorphisms, the fan is said to be a tropical Poincaré duality space. If all the stars of faces also are such spaces, such as for fans of matroids, the fan is called a local tropical Poincaré duality space. In this article, we first give some necessary conditions for fans to be tropical Poincaré duality spaces and a classification in dimension one. Next, we prove that tropical Poincaré duality for the

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2

Leśnik, Karol, and Lech Maligranda. "Abstract Cesàro spaces. Duality." Journal of Mathematical Analysis and Applications 424, no. 2 (2015): 932–51. http://dx.doi.org/10.1016/j.jmaa.2014.11.023.

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3

Gonz�lez, Juan Antonio Navarro. "Duality and finite spaces." Order 6, no. 4 (1990): 401–8. http://dx.doi.org/10.1007/bf00346134.

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4

Maio, Giuseppe Di, Enrico Meccariello, and Somashekhar A. Naimpally. "Duality in Function Spaces." Mediterranean Journal of Mathematics 3, no. 2 (2006): 189–204. http://dx.doi.org/10.1007/s00009-006-0072-z.

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5

BRUHN, HENNING, and MAYA STEIN. "Duality of Ends." Combinatorics, Probability and Computing 19, no. 1 (2009): 47–60. http://dx.doi.org/10.1017/s0963548309990320.

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We investigate the end spaces of infinite dual graphs. We show that there exists a natural homeomorphism * between the end spaces of a graph and its dual, and that * preserves the ‘end degree’. In particular, * maps thick ends to thick ends. Along the way, we prove that Tutte-connectivity is invariant under taking (infinite) duals.

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6

Dimov, Georgi, and Elza Ivanova-Dimova. "Two extensions of the stone duality to the category of zero-dimensional Hausdorff spaces." Filomat 35, no. 6 (2021): 1851–78. http://dx.doi.org/10.2298/fil2106851d.

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Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also the Tarski Duality Theorem; the latter is even derived from one of them. We prove as well two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps. Also, we describe two categories which are dually equivalent to the category ZComp of zero-dimensional Hausdorff compactifications of zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimens

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7

Bhatt, Biseswar Prasad. "Maximal Duality Mappings On Banach Spaces." Journal of Development Review 9, no. 1 (2024): 34–41. http://dx.doi.org/10.3126/jdr.v9i1.69039.

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The analytical features of a Banach space K are characterized by the duality mappings on a Banach space K. One example of a monotone duality mapping on K is the subdifferential of proper convex functions on K. In this case, we look at various instances of normalized duality mappings as well as the idea of monotone operators on K. The surjectivity of the duality mappings and the notions of hemicontinuity and demicontinuity are crucial. If A and B are two monotone mappings then their sum is always monotone mapping but the sum of maximal monotone mapping may not be maximal in general. Ultimately,

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8

Väisälä, Jussi. "Metric duality in Euclidean spaces." MATHEMATICA SCANDINAVICA 80 (December 1, 1997): 249. http://dx.doi.org/10.7146/math.scand.a-12620.

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9

Zhan, Mujun, and Guangfu Cao. "DUALITY OF QK-TYPE SPACES." Bulletin of the Korean Mathematical Society 51, no. 5 (2014): 1411–23. http://dx.doi.org/10.4134/bkms.2014.51.5.1411.

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10

MALAFOSSE, Bruno de. "Duality of new sequence spaces." Hokkaido Mathematical Journal 32, no. 3 (2003): 643–60. http://dx.doi.org/10.14492/hokmj/1350659160.

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11

Kosarew, Siegmund. "Nonabelian duality on Stein spaces." American Journal of Mathematics 120, no. 3 (1998): 637–48. http://dx.doi.org/10.1353/ajm.1998.0024.

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12

González, Manuel, and Antonio Martínez-Abejón. "Local duality for Banach spaces." Expositiones Mathematicae 33, no. 2 (2015): 135–83. http://dx.doi.org/10.1016/j.exmath.2014.04.002.

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13

Ramachandran, D., and L. Rüschendorf. "Duality and perfect probability spaces." Proceedings of the American Mathematical Society 124, no. 7 (1996): 2223–28. http://dx.doi.org/10.1090/s0002-9939-96-03462-4.

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14

Baboolal, D., and Partha Pratim Ghosh. "A duality involving Borel spaces." Journal of Logic and Algebraic Programming 76, no. 2 (2008): 209–15. http://dx.doi.org/10.1016/j.jlap.2008.02.009.

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15

Di Scala, Antonio J., and Andrea Loi. "Symplectic duality of symmetric spaces." Advances in Mathematics 217, no. 5 (2008): 2336–52. http://dx.doi.org/10.1016/j.aim.2007.10.009.

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16

Gryc, William E., and Todd Kemp. "Duality in Segal–Bargmann spaces." Journal of Functional Analysis 261, no. 6 (2011): 1591–623. http://dx.doi.org/10.1016/j.jfa.2011.05.014.

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17

Talponen, Jarno. "Duality of ODE-determined norms." MATHEMATICA SCANDINAVICA 124, no. 1 (2019): 61–80. http://dx.doi.org/10.7146/math.scand.a-109390.

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Recently the author initiated a novel approach to varying exponent Lebesgue space $L^{p(\cdot)}$ norms. In this approach the norm is defined by means of weak solutions to suitable first order ordinary differential equations (ODE). The resulting norm is equivalent with constant $2$ to a corresponding Nakano norm but the norms do not coincide in general and thus their isometric properties are different. In this paper the duality of these ODE-determined $L^{p(\cdot)}$ spaces is investigated. It turns out that the duality of the classical $L^p$ spaces generalizes nicely to this class of spaces. He

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18

Ahmad, Izhar, Divya Agarwal, and Kumar Gupta. "Symmetric duality in complex spaces over cones." Yugoslav Journal of Operations Research, no. 00 (2021): 4. http://dx.doi.org/10.2298/yjor2005015004a.

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Duality theory plays an important role in optimization theory. It has been extensively used for many theoretical and computational problems in mathematical programming. In this paper duality results are established for first and second order Wolfe and Mond-Weir type symmetric dual programs over general polyhedral cones in complex spaces. Corresponding duality relations for nondifferentiable case are also stated. This work will also remove inconsistencies in the earlier work from the literature.

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19

Piękosz, Artur. "Esakia Duality for Heyting Small Spaces." Symmetry 14, no. 12 (2022): 2567. http://dx.doi.org/10.3390/sym14122567.

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We continue our research plan of developing the theory of small and locally small spaces, proposing this theory as a realisation of Grothendieck’s idea of tame topology on the level of general topology. In this paper, we develop the theory of Heyting small spaces and prove a new version of Esakia Duality for such spaces. To do this, we notice that spectral spaces may be seen as sober small spaces with all smops compact and introduce the method of the standard spectralification. This helps to understand open continuous definable mappings between definable spaces over o-minimal structures.

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20

Brodskiy, A. G. "Gale Duality and the Neighborliness of Random Polytopes. I." Modeling and Analysis of Information Systems 19, no. 2 (2015): 62–86. http://dx.doi.org/10.18255/1818-1015-2012-2-62-86.

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21

LAWSON, JIMMIE. "Stably compact spaces." Mathematical Structures in Computer Science 21, no. 1 (2010): 125–69. http://dx.doi.org/10.1017/s0960129510000319.

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The purpose of this paper is to develop the basic theory of stably compact spaces (viz. compact, locally compact, coherent sober spaces) and introduce in an accessible manner and with a minimum of prerequisites some significant new lines of investigation and application arising from recent research, which has arisen primarily in the theoretical computer science community. Three primary themes have developed: (i)the property of stable compactness is preserved under a large variety of constructions involving powerdomains, hyperspaces and function spaces;(ii)the underlying de Groot duality of sta

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22

Bonsangue, Marcello M., Bart Jacobs, and Joost N. Kok. "Duality beyond sober spaces: Topological spaces and observation frames." Theoretical Computer Science 151, no. 1 (1995): 79–124. http://dx.doi.org/10.1016/0304-3975(95)00048-2.

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23

Geske, Christian. "Algebraic intersection spaces." Journal of Topology and Analysis 12, no. 04 (2019): 1157–94. http://dx.doi.org/10.1142/s1793525319500778.

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We define a variant of intersection space theory that applies to many compact complex and real analytic spaces [Formula: see text], including all complex projective varieties; this is a significant extension to a theory which has so far only been shown to apply to a particular subclass of spaces with smooth singular sets. We verify existence of these so-called algebraic intersection spaces and show that they are the (reduced) chain complexes of known topological intersection spaces in the case that both exist. We next analyze “local duality obstructions,” which we can choose to vanish, and ver

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24

Le Merdy, Christian. "On the Duality of Operator Spaces." Canadian Mathematical Bulletin 38, no. 3 (1995): 334–46. http://dx.doi.org/10.4153/cmb-1995-049-9.

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AbstractWe prove that given an operator space structure on a dual Banach space Y*, it is not necessarily the dual one of some operator space structure on Y. This allows us to show that Sakai's theorem providing the identification between C*-algebras having a predual and von Neumann algebras does not extend to the category of operator spaces. We also include a related result about completely bounded operators from B(ℓ2)* into the operator Hilbert space OH.

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25

Roudenko, Svetlana. "Duality of matrix-weighted Besov spaces." Studia Mathematica 160, no. 2 (2004): 129–56. http://dx.doi.org/10.4064/sm160-2-3.

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26

Cobos, Fernando. "Duality and Lorentz-Marcinkiewicz operator spaces." MATHEMATICA SCANDINAVICA 63 (June 1, 1988): 261. http://dx.doi.org/10.7146/math.scand.a-12239.

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27

Khimshiashvili, Giorgi, Gaiane Panina, and Dirk Siersma. "Area-perimeter duality in polygon spaces." MATHEMATICA SCANDINAVICA 127, no. 2 (2021): 252–63. http://dx.doi.org/10.7146/math.scand.a-126041.

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Two natural foliations, guided by area and perimeter, of the configurations spaces of planar polygons are considered and the topology of their leaves is investigated in some detail. In particular, the homology groups and the homotopy type of leaves are determined. The homology groups of the spaces of polygons with fixed area and perimeter are also determined. Besides, we extend the classical isoperimetric duality to all critical points. In conclusion a few general remarks on dual extremal problems in polygon spaces and beyond are given.

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28

Banica, Teodor. "Tannakian Duality for Affine Homogeneous Spaces." Canadian Mathematical Bulletin 61, no. 3 (2018): 483–94. http://dx.doi.org/10.4153/cmb-2017-084-3.

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AbstractAssociated with any closed quantum subgroup and any index set I ⊂ {1,…,N} is a certain homogeneous space , called an affine homogeneous space. Using Tannakian duality methods, we discuss the abstract axiomatization of the algebraic manifolds that can appear in this way.

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29

Tradler, Thomas, and Mahmoud Zeinalian. "Infinity structure of Poincaré duality spaces." Algebraic & Geometric Topology 7, no. 1 (2007): 233–60. http://dx.doi.org/10.2140/agt.2007.7.233.

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30

Antoniuk, Sylwia, and Paweł Waszkiewicz. "A duality of generalized metric spaces." Topology and its Applications 158, no. 17 (2011): 2371–81. http://dx.doi.org/10.1016/j.topol.2011.04.013.

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31

Chakrabarti, D., L. D. Edholm, and J. D. McNeal. "Duality and approximation of Bergman spaces." Advances in Mathematics 341 (January 2019): 616–56. http://dx.doi.org/10.1016/j.aim.2018.10.041.

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32

Ruppenthal, Jean, Håkan Samuelsson Kalm, and Elizabeth Wulcan. "Explicit Serre duality on complex spaces." Advances in Mathematics 305 (January 2017): 1320–55. http://dx.doi.org/10.1016/j.aim.2016.10.013.

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33

KALLEL, Samir. "Duality of generalized Dunkl-Lipschitz spaces." Acta Mathematica Scientia 37, no. 6 (2017): 1567–93. http://dx.doi.org/10.1016/s0252-9602(17)30092-9.

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34

Weaver, Nik. "Duality for Locally Compact Lipschitz Spaces." Rocky Mountain Journal of Mathematics 26, no. 1 (1996): 337–53. http://dx.doi.org/10.1216/rmjm/1181072120.

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35

Mauro, Patricia Couto G., and Dinamerico P. Pombo Jr. "On duality in linearly topologized spaces." International Mathematical Forum 9 (2014): 1041–52. http://dx.doi.org/10.12988/imf.2014.45105.

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36

van der Put, Marius. "Serre duality for rigid analytic spaces." Indagationes Mathematicae 3, no. 2 (1992): 219–35. http://dx.doi.org/10.1016/0019-3577(92)90011-9.

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37

Kamińska, Anna, and Yves Raynaud. "Abstract Lorentz spaces and Köthe duality." Indagationes Mathematicae 30, no. 4 (2019): 553–95. http://dx.doi.org/10.1016/j.indag.2019.02.002.

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38

Christensen, Ole, Xiang Chun Xiao, and Yu Can Zhu. "Characterizing R-duality in Banach spaces." Acta Mathematica Sinica, English Series 29, no. 1 (2012): 75–84. http://dx.doi.org/10.1007/s10114-012-1199-4.

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39

Giribet, Juan Ignacio, Alejandra Maestripieri, and Francisco Martínez Pería. "Duality for frames in Krein spaces." Mathematische Nachrichten 291, no. 5-6 (2018): 879–96. http://dx.doi.org/10.1002/mana.201700149.

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40

Vályi, István. "Strict approximate duality in vector spaces." Applied Mathematics and Computation 25, no. 3 (1988): 227–46. http://dx.doi.org/10.1016/0096-3003(88)90074-4.

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41

Sun, S. H. "Duality on Compact Prime Ringed Spaces." Journal of Algebra 169, no. 3 (1994): 805–16. http://dx.doi.org/10.1006/jabr.1994.1309.

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42

Shanker, Gauree. "The L-dual of a Generalized m-Kropina Space." Journal of the Tensor Society 5, no. 01 (2007): 15–25. http://dx.doi.org/10.56424/jts.v5i01.10445.

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In 1987, R. Miron introduced the concept of L-duality between Cartan spaces and Finsler spaces ([5]) : The geometry of higher order Finsler spaces were sudied in ([1] ; [8]) : The theory of higher order Lagrange and Hamilton spaces were discussed in ([6] ; [7] ; [9]) : Some special problems concerning the L- duality and classes of Finsler spaces were studied in ([3] ; [13]) : In ([2] ; [10] ; [11]) the L-duals of Randers, Kropina and Matsumoto space were introduced. The L-dual of an (®; ¯) Finsler space was introduced in [12] :In this paper we give the L-dual of a generalized m-Kropina Space.

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43

Fouché, Willem L. "Ramsey actions and Gelfand duality." Pure Mathematics and Applications 30, no. 3 (2022): 13–27. http://dx.doi.org/10.2478/puma-2022-0020.

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Abstract In this paper we discuss structural Ramsey theory and how it relates to the understanding of extremely amenable groups with an emphasis on the measure theoretic nature of this problem. We discuss the problem within Blass-Ramsey actions on discrete spaces and and more general group actions on compact spaces and explore how we can look at these problems by looking at Gelfand duals of commutative C *-algebras.

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44

Xia, Runlian, and Xiao Xiong. "Operator-valued local Hardy spaces." Journal of Operator Theory 82, no. 2 (2019): 383–443. http://dx.doi.org/10.7900/jot.2018jun02.2191.

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This paper gives a systematic study of operator-valued local\break Hardy spaces, which are localizations of the Hardy spaces defined by Mei. We prove the h1-bmo duality and the hp-hq duality for any conjugate pair (p,q) when p∈(1,∞). We show that h1(Rd,M) and bmo(Rd,M) are also good endpoints of Lp(L∞(Rd)¯¯¯¯⊗M) for interpolation. We obtain the local version of Calder\'on--Zygmund theory, and then deduce that the Poisson kernel in our definition of the local Hardy norms can be replaced by any reasonable test function. Finally, we establish the atomic decomposition of the local Hardy space hc1(

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45

Jell, Philipp, Kristin Shaw, and Jascha Smacka. "Superforms, tropical cohomology, and Poincaré duality." Advances in Geometry 19, no. 1 (2019): 101–30. http://dx.doi.org/10.1515/advgeom-2018-0006.

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AbstractWe establish a canonical isomorphism between two bigraded cohomology theories for polyhedral spaces: Dolbeault cohomology of superforms and tropical cohomology. Furthermore, we prove Poincaré duality for cohomology of tropical manifolds, which are polyhedral spaces locally given by Bergman fans of matroids.

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46

Carai, Luca. "New Directions in Duality Theory for Modal Logic." Bulletin of Symbolic Logic 27, no. 4 (2021): 527. http://dx.doi.org/10.1017/bsl.2021.52.

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AbstractIn this work we present some new contributions towards two different directions in the study of modal logic. First we employ tense logics to provide a temporal interpretation of intuitionistic quantifiers as “always in the future” and “sometime in the past.” This is achieved by modifying the Gödel translation and resolves an asymmetry between the standard interpretation of intuitionistic quantifiers.Then we generalize the classic Gelfand–Naimark–Stone duality between compact Hausdorff spaces and uniformly complete bounded archimedean $\ell $ -algebras to a duality encompassing compact

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47

GOUBAULT-LARRECQ, JEAN. "De Groot duality and models of choice: angels, demons and nature." Mathematical Structures in Computer Science 20, no. 2 (2010): 169–237. http://dx.doi.org/10.1017/s0960129509990363.

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We introduce convex–concave duality for various models of non-deterministic choice, probabilistic choice and the two of them combined. This complements the well-known duality of stably compact spaces in a pleasing way: convex–concave duality swaps angelic and demonic choice, and leaves probabilistic choice invariant.

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48

BEZHANISHVILI, NICK, and WESLEY H. HOLLIDAY. "CHOICE-FREE STONE DUALITY." Journal of Symbolic Logic 85, no. 1 (2019): 109–48. http://dx.doi.org/10.1017/jsl.2019.11.

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AbstractThe standard topological representation of a Boolean algebra via the clopen sets of a Stone space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal Theorem. In this article, we describe a choice-free topological representation of Boolean algebras. This representation uses a subclass of the spectral spaces that Stone used in his representation of distributive lattices via compact open sets. It also takes advantage of Tarski’s observation that the regular open sets of any topological space form a Boolean algebra. We prove without choice principles that an

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49

Noi, Takahiro. "Duality of Variable Exponent Triebel-Lizorkin and Besov Spaces." Journal of Function Spaces and Applications 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/361807.

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We will prove the duality and reflexivity of variable exponent Triebel-Lizorkin and Besov spaces. It was shown by many authors that variable exponent Triebel-Lizorkin spaces coincide with variable exponent Bessel potential spaces, Sobolev spaces, and Lebesgue spaces when appropriate indices are chosen. In consequence of the results, these variable exponent function spaces are shown to be reflexive.

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50

Cobos, Fernando, and Luz M. Fernández-Cabrera. "Duality for logarithmic interpolation spaces and applications to Besov spaces." Banach Center Publications 119 (2019): 109–22. http://dx.doi.org/10.4064/bc119-5.

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