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Journal articles on the topic 'Hyperspace – Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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1

Curtis, D. W. "Application of a Selection Theorem to Hyperspace Contractibility." Canadian Journal of Mathematics 37, no. 4 (August 1, 1985): 747–59. http://dx.doi.org/10.4153/cjm-1985-040-7.

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For X a metric continuum, 2X denotes the hyper space of all nonempty subcompacta, with the topology induced by the Hausdorff metric H, and C(X) ⊂ 2X the hyperspace of subcontinua. These hyperspaces are continua, in fact are arcwise-connected, since there exist order arcs between each hyperspace element and the element X. They also have trivial shape, i.e., maps of the hyperspaces into ANRs are homotopic to constant maps. For a detailed discussion of these and other general hyperspace properties, we refer the reader to Nadler's monograph [4].The question of hyperspace contractibility was first considered by Wojdyslawski [8], who showed that 2X and C(X) are contractible if X is locally connected. Kelley [2] gave a more general condition (now called property K) which is sufficient, but not necessary, for hyperspace contractibility. The continuum X has property K if for every there exists δ > 0 such that, for every pair of points x, y with d(x, y) < δ and every subcontinuum M containing x, there exists a subcontinuum N containing y with .

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2

Morales, José Ángel Juárez, Gerardo Reyna Hernández, Jesús Romero Valencia, and Omar Rosario Cayetano. "Free Cells in Hyperspaces of Graphs." Mathematics 9, no. 14 (July 10, 2021): 1627. http://dx.doi.org/10.3390/math9141627.

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Often for understanding a structure, other closely related structures with the former are associated. An example of this is the study of hyperspaces. In this paper, we give necessary and sufficient conditions for the existence of finitely-dimensional maximal free cells in the hyperspace C(G) of a dendrite G; then, we give necessary and sufficient conditions so that the aforementioned result can be applied when G is a dendroid. Furthermore, we prove that the arc is the unique arcwise connected, compact, and metric space X for which the anchored hyperspace Cp(X) is an arc for some p∈X.

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3

Costantini, C., S. Levi, and J. Pelant. "Infima of hyperspace topologies." Mathematika 42, no. 1 (June 1995): 67–86. http://dx.doi.org/10.1112/s0025579300011360.

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4

BERAN, ZDENĚK, and SERGEJ ČELIKOVSKÝ. "CHAOS ON HYPERSPACE." International Journal of Bifurcation and Chaos 23, no. 05 (May 2013): 1350084. http://dx.doi.org/10.1142/s0218127413500843.

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In this paper, the chaotic behavior of a set-valued mapping F : X → 2X, where X is a compact space, is investigated. The existence of the generalized shadowing property in the hyperspace 2X is proved. Based on the generalized shadowing property of the set-valued mappings F and the assumption of the existence of an unstable chain recurrent point of the mapping F, it is shown that the Bernoulli system of bi-directional shifts is embedded in the sense of semiconjugacy into the image of mapping F, i.e. Smale's chaos in the set-valued system F is thereby proved.

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5

Ingram, W. T., and D. D. Sherling. "Two Continua Having A Property of J. L. Kelley." Canadian Mathematical Bulletin 34, no. 3 (September 1, 1991): 351–56. http://dx.doi.org/10.4153/cmb-1991-056-1.

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AbstractIn proving the contractibility of certain hyperspaces J. L. Kelley identified and defined a certain uniformnessproperty which he called Property 3.2. It is known that the classes of locally connected continua, homogeneous continua and hereditarily indecomposable continua have Property 3.2. In this paper we prove that two examples of indecomposable continua developed respectively by the authors have Property 3.2. One is the example of a nonchainable atriodic tree-like continuum with positive span which was defined by the first author, and the other is a nonchainable, noncircle-like continuum which has the cone=hyperspace property which was defined by the second author. Each of the examples is an inverse limit of an inverse system having a single bonding map.

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6

Macías, Sergio, and Sam B. Nadler. "Absolute n-fold hyperspace suspensions." Colloquium Mathematicum 105, no. 2 (2006): 221–31. http://dx.doi.org/10.4064/cm105-2-5.

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7

Banks, John. "Chaos for induced hyperspace maps." Chaos, Solitons & Fractals 25, no. 3 (August 2005): 681–85. http://dx.doi.org/10.1016/j.chaos.2004.11.089.

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8

Maya, David, Patricia Pellicer-Covarrubias, and Roberto Pichardo-Mendoza. "Cardinal functions of the hyperspace of convergent sequences." Mathematica Slovaca 68, no. 2 (April 25, 2018): 431–50. http://dx.doi.org/10.1515/ms-2017-0114.

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Abstract The symbol 𝓢c(X) denotes the hyperspace of all nontrivial convergent sequences in a Hausdorff space X. This hyperspace is endowed with the Vietoris topology. In the current paper, we compare the cellularity, the tightness, the extent, the dispersion character, the net weight, the i-weight, the π-weight, the π-character, the pseudocharacter and the Lindelöf number of 𝓢c(X) with the corresponding cardinal function of X. We also answer a question posed by the authors in a previous paper.

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9

Holá, Lubica. "Embeddings in the Fell and Wijsman topologies." Filomat 33, no. 9 (2019): 2747–50. http://dx.doi.org/10.2298/fil1909747h.

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It is shown that if a T2 topological space X contains a closed uncountable discrete subspace, then the spaces (?1 + 1)? and (?1 + 1)?1 embed into (CL(X),?F), the hyperspace of nonempty closed subsets of X equipped with the Fell topology. If (X, d) is a non-separable perfect topological space, then (?1 + 1)? and (?1 +1)?1 embed into (CL(X), ?w(d)), the hyperspace of nonempty closed subsets of X equipped with the Wijsman topology, giving a partial answer to the Question 3.4 in [2].

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10

Shapiro, L. B. "The category characteristic of a hyperspace." Russian Mathematical Surveys 43, no. 4 (August 31, 1988): 233–34. http://dx.doi.org/10.1070/rm1988v043n04abeh001901.

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11

Escobedo, Raúl, Patricia Pellicer-Covarrubias, and Vicente Sánchez-Gutiérrez. "The hyperspace of totally disconnected sets." Glasnik Matematicki 55, no. 1 (June 12, 2020): 113–28. http://dx.doi.org/10.3336/gm.55.1.10.

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12

Künzi, Hans-Peter A. "Iterations of quasi-uniform hyperspace constructions." Acta Mathematica Hungarica 113, no. 3 (November 2006): 213–25. http://dx.doi.org/10.1007/s10474-006-0100-2.

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13

Cánovas Peña, Jose S., and Gabriel Soler López. "Topological entropy for induced hyperspace maps." Chaos, Solitons & Fractals 28, no. 4 (May 2006): 979–82. http://dx.doi.org/10.1016/j.chaos.2005.08.173.

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14

Lončar, Ivan. "Arcwise Connected Continua and Whitney Maps." gmj 12, no. 2 (June 2005): 321–30. http://dx.doi.org/10.1515/gmj.2005.321.

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Abstract Let 𝑋 be a non-metric continuum, and 𝐶(𝑋) be the hyperspace of subcontinua of 𝑋. It is known that there is no Whitney map on the hyperspace 2𝑋 for non-metric Hausdorff compact spaces 𝑋. On the other hand, there exist non-metric continua which admit and ones which do not admit a Whitney map for 𝐶(𝑋). In particular, a locally connected or a rimmetrizable continuum 𝑋 admits a Whitney map for 𝐶(𝑋) if and only if it is metrizable. In this paper we investigate the properties of continua 𝑋 which admit a Whitney map for 𝐶(𝑋) or for 𝐶2(𝑋).

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15

GINGL, ZOLTAN, LASZLO B. KISH, and SUNIL P. KHATRI. "TOWARDS BRAIN-INSPIRED COMPUTING." Fluctuation and Noise Letters 09, no. 04 (December 2010): 403–12. http://dx.doi.org/10.1142/s0219477510000332.

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We present introductory considerations and analysis toward computing applications based on the recently introduced deterministic logic scheme with random spike (pulse) trains [Phys. Lett. A373 (2009) 2338–2342]. Also, in considering the questions, "why random?" and "why pulses?", we show that the random pulse based scheme provides the advantages of realizing multivalued deterministic logic. Pulse trains are realized by an element called orthogonator. We discuss two different types of orthogonators, parallel (intersection-based) and serial (demultiplexer-based) orthogonators. The last one can be slower but it makes sequential logic design straightforward. We propose generating a multidimensional logic hyperspace [Phys. Lett. A373 (2009) 1928–1934] by using the zero-crossing events of uncorrelated Gaussian electrical noises available in the chips. The spike trains in the hyperspace are non-overlapping, and are referred to as neuro-bits. To demonstrate this idea, we generate three-dimensional hyperspace bases using the zero-crossing events of two uncorrelated Gaussian noise sources. In such a scenario, the detection of different hyperspace basis elements may have vastly differing delays. We show that it is possible to provide an identical speed for the detection of all the hyperspace bases elements using correlated noise sources, and demonstrate this for the two neuro-bits situation. The key impact of this paper is to demonstrate that a logic design approach using such neuro-bits can yield a fast, low power and environmental variation tolerant means of designing computer circuitry. It also enables the realization of multivalued logic, and also significantly increasing the complexity of computer circuits by allowing several neuro-bits to be transmitted on a single wire.

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16

Bazilevich, L. E. "Hyperspace of max-plus convex compact sets." Mathematical Notes 84, no. 5-6 (December 2008): 615–22. http://dx.doi.org/10.1134/s0001434608110023.

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17

Zhang, Gengrong, Fanping Zeng, and Xinhe Liu. "Devaney’s chaotic on induced maps of hyperspace." Chaos, Solitons & Fractals 27, no. 2 (January 2006): 471–75. http://dx.doi.org/10.1016/j.chaos.2005.03.053.

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18

Beer, Gerald, Alojzy Lechicki, Sandro Levi, and Somashekhar Naimpally. "Distance functional and suprema of hyperspace topologies." Annali di Matematica Pura ed Applicata 162, no. 1 (December 1992): 367–81. http://dx.doi.org/10.1007/bf01760016.

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19

PEPER, FERDINAND, and LASZLO B. KISH. "INSTANTANEOUS, NON-SQUEEZED, NOISE-BASED LOGIC." Fluctuation and Noise Letters 10, no. 02 (June 2011): 231–37. http://dx.doi.org/10.1142/s0219477511000521.

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Noise-based logic, by utilizing its multidimensional logic hyperspace, has significant potential for parallel operations in beyond-Moore-chips. However universal gates for Boolean logic thus far had to rely on either time averaging to distinguish signals from each other or, alternatively, on squeezed logic signals, where the logic-high was represented by a random process and the logic-low was a zero signal. A major setback is that squeezed logic variables are unable to work in the hyperspace, because the logic-low zero value sets the hyperspace product vector to zero. This paper proposes Boolean universal logic gates that alleviate such shortcomings. They are able to work with non-squeezed logic values where both the high and low values are encoded into nonzero, bipolar, independent random telegraph waves. Non-squeezed universal Boolean logic gates for spike-based brain logic are also shown. The advantages versus disadvantages of the two logic types are compared.

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20

Gilson, James G. "Classical fluid aspects of nonlinear Schrödinger equations and solitons." Journal of Applied Mathematics and Simulation 1, no. 2 (January 1, 1987): 99–114. http://dx.doi.org/10.1155/s1048953388000085.

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The author extends his alternative theory for Schrödinger quantum mechanics by introducing the idea of energy reference strata over configuration space. It is then shown that the view from various such strata defines, the content of the system of interest and enables a variety of different descriptions of events in the same space time region. Thus according to the point of view or energy stratum chosen so the type of Schrödinger equation, linear or otherwise, appropriate to describe the system is determined. A nonlinear information channel between two dimensional fluid action in hyperspace into two dimensional energy hyperspace is shown to exist generally as a background to nonlinear Schrödinger structures. In addition it is shown how soliton solutions of the one dimensional Schrödinger equation are related to two dimensional vortex fields in hyperspace.

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21

Naimpally, S. A., and P. L. Sharma. "Fine uniformity and the locally finite hyperspace topology." Proceedings of the American Mathematical Society 103, no. 2 (February 1, 1988): 641. http://dx.doi.org/10.1090/s0002-9939-1988-0943098-9.

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22

Costantini, C., S. Levi, and J. Zieminska. "Metrics that generate the same hyperspace convergence." Set-Valued Analysis 1, no. 2 (1993): 141–57. http://dx.doi.org/10.1007/bf01027689.

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23

Bernardes, Nilson C., and Rômulo M. Vermersch. "Hyperspace Dynamics of Generic Maps of the Cantor Space." Canadian Journal of Mathematics 67, no. 2 (April 2015): 330–49. http://dx.doi.org/10.4153/cjm-2014-005-5.

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AbstractWe study the hyperspace dynamics induced fromgeneric continuous maps and fromgeneric homeomorphisms of the Cantor space, with emphasis on the notions of Li– Yorke chaos, distributional chaos, topological entropy, chain continuity, shadowing, and recurrence.

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24

Loncar, Ivan. "Non-metric Rim-metrizable continua and unique hyperspace." Publications de l'Institut Mathematique 73, no. 87 (2003): 97–113. http://dx.doi.org/10.2298/pim0373097l.

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25

Czajko, Jakub. "Elie Cartan and pan-geometry of multispatial hyperspace." Chaos, Solitons & Fractals 19, no. 3 (February 2004): 479–502. http://dx.doi.org/10.1016/s0960-0779(03)00254-6.

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26

Mrsevic, Mila, and Milena Jelic. "SELECTION PRINCIPLES AND HYPERSPACE TOPOLOGIES IN CLOSURE SPACES." Journal of the Korean Mathematical Society 43, no. 5 (September 30, 2006): 1099–114. http://dx.doi.org/10.4134/jkms.2006.43.5.1099.

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27

Andres, Jan. "Chaos for multivalued maps and induced hyperspace maps." Chaos, Solitons & Fractals 138 (September 2020): 109898. http://dx.doi.org/10.1016/j.chaos.2020.109898.

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28

Holá, L’ubica, and László Zsilinszky. "On generalized metric properties of the Fell hyperspace." Annali di Matematica Pura ed Applicata (1923 -) 194, no. 5 (April 29, 2014): 1259–67. http://dx.doi.org/10.1007/s10231-014-0418-2.

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29

Antonyan, Sergey A. "The Gromov-Hausdorff hyperspace of a Euclidean space." Advances in Mathematics 363 (March 2020): 106977. http://dx.doi.org/10.1016/j.aim.2020.106977.

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30

José G., Anaya, Castañeda-Alvarado Enrique, and Martínez-Cortez José A. "On the hyperspace $C_n(X)/{C_n}_K(X)$." Commentationes Mathematicae Universitatis Carolinae 62, no. 2 (August 3, 2021): 201–24. http://dx.doi.org/10.14712/1213-7243.2021.018.

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31

Costantini, Camillo. "On the hyperspace of a non-separable metric space." Proceedings of the American Mathematical Society 126, no. 11 (1998): 3393–96. http://dx.doi.org/10.1090/s0002-9939-98-04956-9.

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32

Belegradek, Igor. "The Gromov-Hausdorff hyperspace of nonnegatively curved $2$-spheres." Proceedings of the American Mathematical Society 146, no. 4 (November 13, 2017): 1757–64. http://dx.doi.org/10.1090/proc/13910.

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33

Hu, Thakyin, and Jen-Chun Fang. "Weak topology and Browder–Kirk's theorem on hyperspace." Journal of Mathematical Analysis and Applications 334, no. 2 (October 2007): 799–803. http://dx.doi.org/10.1016/j.jmaa.2006.12.078.

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34

Macias, Sergio. "On the n-fold hyperspace suspension of continua, II." Glasnik Matematicki 41, no. 2 (December 15, 2006): 335–43. http://dx.doi.org/10.3336/gm.41.2.16.

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35

Macias, Juan Carlos. "On the n-fold pseudo-hyperspace suspensions of continua." Glasnik Matematicki 43, no. 2 (November 9, 2008): 439–49. http://dx.doi.org/10.3336/gm.43.2.14.

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36

Illanes, Alejandro, and Jorge M. Martinez-Montejano. "Compactifications of [0,infinity) with unique hyperspace Fn(X)." Glasnik Matematicki 44, no. 2 (December 9, 2009): 457–78. http://dx.doi.org/10.3336/gm.44.2.12.

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37

Brandsma, Henno, and Jan van Mill. "A compact HL-space need not have a monolithic hyperspace." Proceedings of the American Mathematical Society 126, no. 11 (1998): 3407–11. http://dx.doi.org/10.1090/s0002-9939-98-04374-3.

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38

Illanes, Alejandro. "A continuum whose hyperspace of subcontinua is not $g$-contractible." Proceedings of the American Mathematical Society 130, no. 7 (February 12, 2002): 2179–82. http://dx.doi.org/10.1090/s0002-9939-02-06307-4.

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39

Hou, Ji-Cheng, and Paolo Vitolo. "Fell topology on the hyperspace of a non-Hausdorff space." Ricerche di Matematica 57, no. 1 (June 6, 2008): 111–25. http://dx.doi.org/10.1007/s11587-008-0032-y.

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40

Gnitetskaya, Tatyana N., and Elena B. Ivanova. "Interdisciplinary Conceptual Cluster in Mathematics and Physics on the Basis of a Graph Model of Interdisciplinary Links." Advanced Materials Research 889-890 (February 2014): 1704–7. http://dx.doi.org/10.4028/www.scientific.net/amr.889-890.1704.

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This paper describes a method of forming an interdisciplinary conceptual cluster in mathematics and physics on the basis of a graph model of interdisciplinary links developed by T.N. Gnitetskaya. Interdisciplinary hyperspace for mathematics and physics courses for engineering majors according to the group of concepts was built. In the framework of the model, quantitative characteristics of interdisciplinary links were evaluated, using which a hierarchy of clusters content was established and the fundamental unit of concepts was emphasized. A quantitative meaning of "capacity" of an interdisciplinary conceptual cluster of mathematics and physics courses according to the group of concepts was achieved.

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41

Bell, Murray, and Jan Pelant. "Continuous Images of Compact Semilattices." Canadian Mathematical Bulletin 30, no. 1 (March 1, 1987): 109–13. http://dx.doi.org/10.4153/cmb-1987-016-4.

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AbstractHyadic spaces are the continuous images of a hyperspace of a compact space. We prove that every non-isolated point in a hyadic space is the endpoint of some infinite cardinal subspace. We isolate a more general order-theoretic property of hyerspaces of compact spaces which is also enjoyed by compact semilattices from which the theorem follows.

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42

Rosa, Marco, and Paolo Vitolo. "Comparability of lower Attouch-Wets topologies." Filomat 31, no. 5 (2017): 1435–40. http://dx.doi.org/10.2298/fil1705435r.

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Beer and Di Concilio [4] have given necessary and sufficient conditions for a two-sided Attouch-Wets topology to contain another on the hyperspace of non-empty closed subsets of a metrizable space as determined by metrics compatible with the topology. In the present paper, we characterize comparability of lower Attouch-Wets topologies as determined by compatible metrics.

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43

Hu, Jennifer Shueh-Inn, and Thakyin Hu. "Krein-Milman's Extreme Point Theorem and Weak Topology on Hyperspace." Taiwanese Journal of Mathematics 20, no. 3 (May 2016): 629–38. http://dx.doi.org/10.11650/tjm.20.2016.6411.

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44

Bazilevich, L. E. "Topology of the hyperspace of convex bodies of constant width." Mathematical Notes 62, no. 6 (December 1997): 683–87. http://dx.doi.org/10.1007/bf02355455.

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45

Cao, Jiling, and Jesús Rodríguez-López. "On hyperspace topologies via distance functionals in quasi-metric spaces." Acta Mathematica Hungarica 112, no. 3 (September 2006): 249–68. http://dx.doi.org/10.1007/s10474-006-0077-x.

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46

PANOV, E. YU. "EXISTENCE OF STRONG TRACES FOR GENERALIZED SOLUTIONS OF MULTIDIMENSIONAL SCALAR CONSERVATION LAWS." Journal of Hyperbolic Differential Equations 02, no. 04 (December 2005): 885–908. http://dx.doi.org/10.1142/s0219891605000658.

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In the half-space t > 0 a multidimensional scalar conservation law with only continuous flux vector is considered. For the wide class of functions including generalized entropy sub- and super-solutions to this equation, we prove existence of the strong trace on the initial hyperspace t = 0. No nondegeneracy conditions on the flux are required.

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47

Illanes, Alejandro. "A continuum whose hyperspace of subcontinua is not its continuous image." Proceedings of the American Mathematical Society 135, no. 12 (December 1, 2007): 4019–23. http://dx.doi.org/10.1090/s0002-9939-07-08695-9.

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48

Bella, A. "Some cardinality properties of a hyperspace with the locally finite topology." Proceedings of the American Mathematical Society 104, no. 4 (April 1, 1988): 1274. http://dx.doi.org/10.1090/s0002-9939-1988-0969059-1.

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49

Liu, Lei, and Shuli Zhao. "Martelli’s Chaos in Inverse Limit Dynamical Systems and Hyperspace Dynamical Systems." Results in Mathematics 63, no. 1-2 (August 14, 2011): 195–207. http://dx.doi.org/10.1007/s00025-011-0188-8.

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50

Illanes, Alejandro. "Hereditarily indecomposable Hausdorff continua have unique hyperspaces 2X and Cn(X)." Publications de l'Institut Math?matique (Belgrade) 89, no. 103 (2011): 49–56. http://dx.doi.org/10.2298/pim1103049i.

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Let X be a Hausdorff continuum (a compact connected Hausdorff space). Let 2X (respectively, Cn(X)) denote the hyperspace of nonempty closed subsets of X (respectively, nonempty closed subsets of X with at most n components), with the Vietoris topology. We prove that if X is hereditarily indecomposable, Y is a Hausdorff continuum and 2X (respectively Cn(X)) is homeomorphic to 2Y (respectively, Cn(Y )), then X is homeomorphic to Y.

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