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Relevant bibliographies by topics / Topological Hypergroups

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Academic literature on the topic 'Topological Hypergroups'

Author: Grafiati

Published: 18 May 2024

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Journal articles on the topic "Topological Hypergroups"

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VOIT, MICHAEL. "CONTINUOUS ASSOCIATION SCHEMES AND HYPERGROUPS." Journal of the Australian Mathematical Society 106, no. 03 (July 27, 2018): 361–426. http://dx.doi.org/10.1017/s1446788718000149.

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Classical finite association schemes lead to finite-dimensional algebras which are generated by finitely many stochastic matrices. Moreover, there exist associated finite hypergroups. The notion of classical discrete association schemes can be easily extended to the possibly infinite case. Moreover, this notion can be relaxed slightly by using suitably deformed families of stochastic matrices by skipping the integrality conditions. This leads to a larger class of examples which are again associated with discrete hypergroups. In this paper we propose a topological generalization of association schemes by using a locally compact basis space $X$ and a family of Markov-kernels on $X$ indexed by some locally compact space $D$ where the supports of the associated probability measures satisfy some partition property. These objects, called continuous association schemes, will be related to hypergroup structures on $D$ . We study some basic results for this notion and present several classes of examples. It turns out that, for a given commutative hypergroup, the existence of a related continuous association scheme implies that the hypergroup has many features of a double coset hypergroup. We, in particular, show that commutative hypergroups, which are associated with commutative continuous association schemes, carry dual positive product formulas for the characters. On the other hand, we prove some rigidity results in particular in the compact case which say that for given spaces $X,D$ there are only a few continuous association schemes.

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Singha, Manoranjan, Kousik Das, and Bijan Davvaz. "On topological complete hypergroups." Filomat 31, no. 16 (2017): 5045–56. http://dx.doi.org/10.2298/fil1716045s.

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One of the main obstacles before the development of the theory of topological hypergroups is the fact that translation of open sets may not be open in this setting. In this paper, we get rid of such obstacle by introducing the concept of topological complete hypergroups and investigate some of their properties.

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3

Abughazalah, Nabilah, Naveed Yaqoob, and Kiran Shahzadi. "Topological Structures of Lower and Upper Rough Subsets in a Hyperring." Journal of Mathematics 2021 (April 14, 2021): 1–6. http://dx.doi.org/10.1155/2021/9963623.

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In this paper, we study the connection between topological spaces, hyperrings (semi-hypergroups), and rough sets. We concentrate here on the topological parts of the lower and upper approximations of hyperideals in hyperrings and semi-hypergroups. We provide the conditions for the boundary of hyp-ideals of a hyp-ring to become the hyp-ideals of hyp-ring.

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Chen, Chung-Chuan, Seyyed Mohammad Tabatabaie, and Ali Mohammadi. "Disjoint topological transitivity for weighted translations generated by group actions." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1229–40. http://dx.doi.org/10.1515/ms-2021-0050.

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Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

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Chen, Chung-Chuan, Seyyed Mohammad Tabatabaie, and Ali Mohammadi. "Disjoint topological transitivity for weighted translations generated by group actions." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1229–40. http://dx.doi.org/10.1515/ms-2021-0050.

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Abstract In this note, we give a sufficient and necessary condition for weighted translations, generated by group actions, to be disjoint topologically transitive in terms of the weights, the group element and the measure. The characterization of disjoint topological mixing is obtained as well. Moreover, we apply the results to the quotient spaces of locally compact groups and hypergroups.

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Ghasemi, Khatereh, and Javad Jamalzadeh. "Hypernormed entropy on topological hypernormed hypergroups." Soft Computing 26, no. 1 (November 19, 2021): 99–104. http://dx.doi.org/10.1007/s00500-021-06434-5.

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7

Heidari, D., B. Davvaz, and S. M. S. Modarres. "Topological Hypergroups in the Sense of Marty." Communications in Algebra 42, no. 11 (May 23, 2014): 4712–21. http://dx.doi.org/10.1080/00927872.2013.821314.

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Jamalzadeh, Javad. "Erratum to “Topological hypergroups in the sense of Marty”." Communications in Algebra 45, no. 3 (October 7, 2016): 1187–88. http://dx.doi.org/10.1080/00927872.2016.1172634.

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9

Medghalchi, A. R. "Cohomology on hypergroup algebras." Studia Scientiarum Mathematicarum Hungarica 39, no. 3-4 (November 1, 2002): 297–307. http://dx.doi.org/10.1556/sscmath.39.2002.3-4.4.

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There are concepts which are related to or can be formulated by homological techniques, such as derivations, multipliers and lifting problems. Moreover, a Banach algebra A is said to be amenable if H1(A,X*)=0 for every A-dual module X*. Another concept related to the theory is the concept of amenability in the sense of Johnson. A topological group G is said to be amenable if there is an invariant mean on L 8(G). Johnson has shown that a topological group is amenable if and only if the group algebra L1(G) is amenable. The aim of this research is to define the cohomology on a hypergroup algebra L(K) and extend the results of L1(G) over to L(K). At first stage it is viewed that Johnson's theorem is not valid so more. If A is a Banach algebra and h is a multiplicative linear functional on A, then (A,h) is called left amenable if for any Banach two-sided A-module X with ax=h(a)x(a? A, x? X),H1(A,X*)=0. We prove that (L(K),h) is left amenable if and only if K is left amenable. Where, the latter means that there is a left invariant mean m on C(K), i. e., m(lf)=m(f)x, where lxf(µ)=f(dx*µ). In this case we briefly say that L(K) is left amenable. Johnson also showed that L1(G) is amenable if and only if the augmentation ideal I={f? L1(G)|∫Gf=0}0 has abounded right approximate identity. We extend this result to hypergroups.

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10

Ardakani, Hamid, and Asieh Pourhaghani. "On geometric space and its applications in topological Hv-groups." Filomat 35, no. 3 (2021): 855–70. http://dx.doi.org/10.2298/fil2103855a.

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We generalize the concept of topological hypergroup to topological Hv-group and define some topologies on Hv-groups by using the concept of geometric space, which was defined by Freni. By applying these topologies, we have always a topological Hv-group without need any more conditions. Moreover, we state some conditions on a topological Hv-group that make it complete. Our aim is to generalize the concept of topological hypergroup to topological Hv-group via considering the characteristics of the induced geometric space.

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Dissertations / Theses on the topic "Topological Hypergroups"

1

Das, Kousik. "Topological Hyperalgebra with special emphasis on Topological Hypergroups." Thesis, University of North Bengal, 2022. http://ir.nbu.ac.in/handle/123456789/5087.

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Kamyabi-Gol, Rajab Ali. "Topological center of dual branch algebras associated to hypergroups." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/nq21584.pdf.

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Book chapters on the topic "Topological Hypergroups"

1

"Topological Hypergroups." In Hypergroup Theory, 239–76. WORLD SCIENTIFIC, 2022. http://dx.doi.org/10.1142/9789811249396_0012.

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