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dc.contributor.author | Shakir, Qays Rashid![]() |
es_ES |
dc.date.accessioned | 2023-05-02T06:14:07Z | |
dc.date.available | 2023-05-02T06:14:07Z | |
dc.date.issued | 2023-04-05 | |
dc.identifier.issn | 1576-9402 | |
dc.identifier.uri | http://hdl.handle.net/10251/193018 | |
dc.description.abstract | [EN] In this article, we investigate the notion of setwise betweenness, a concept introduced by P. Bankston as a generalisation of pointwise betweenness. In the context of continua, we say that a subset C of a continuum X is between distinct points a and b of X if every subcontinuum K of X containing both a and b intersects C. The notion of an interval [a,b] then arises naturally. Further interesting questions are derived from considering such intervals within an associated hyperspace on X. We explore these ideas within the context of the Vietoris topology and n-symmetric product hyperspaces on all nonempty closed subsets of a topological space X, CL(X). Moreover, an alternative pointwise interval, derived from setwise intervals, is introduced. | es_ES |
dc.language | Inglés | es_ES |
dc.publisher | Universitat Politècnica de València | es_ES |
dc.relation.ispartof | Applied General Topology | es_ES |
dc.rights | Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) | es_ES |
dc.subject | Betweenness relation | es_ES |
dc.subject | Road system | es_ES |
dc.subject | Hyperspace | es_ES |
dc.title | On setwise betweenness | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.4995/agt.2023.18061 | |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Shakir, QR. (2023). On setwise betweenness. Applied General Topology. 24(1):115-123. https://doi.org/10.4995/agt.2023.18061 | es_ES |
dc.description.accrualMethod | OJS | es_ES |
dc.relation.publisherversion | https://doi.org/10.4995/agt.2023.18061 | es_ES |
dc.description.upvformatpinicio | 115 | es_ES |
dc.description.upvformatpfin | 123 | es_ES |
dc.type.version | info:eu-repo/semantics/publishedVersion | es_ES |
dc.description.volume | 24 | es_ES |
dc.description.issue | 1 | es_ES |
dc.identifier.eissn | 1989-4147 | |
dc.relation.pasarela | OJS\18061 | es_ES |
dc.description.references | P. Bankston, Road systems and betweenness, Bull. Math. Sci. 3 (2013), 389-408. https://doi.org/10.1007/s13373-013-0040-4 | es_ES |
dc.description.references | P. Bankston, When Hausdorff continua have no gaps, Topology Proc. 44 (2014), 177-188. | es_ES |
dc.description.references | P. Bankston, The antisymmetry betweenness axiom and Hausdorff continua, Topology Proc. 45 (2015), 189-215. | es_ES |
dc.description.references | P. Bankston, Topological betweenness relations, Presentation, Oxford Topology Seminar, (2012). | es_ES |
dc.description.references | G. Birkhoff and S. A. Kiss, A ternary operation in distributive lattices, Bull. Amer. Math. Soc. 53 (1947), 749-752. https://doi.org/10.1090/S0002-9904-1947-08864-9 | es_ES |
dc.description.references | J. Bruno, A. McCluskey and P. Szeptycki, Betweenness relations in a categorical setting, Results Math. 72 (2017), 649-664. https://doi.org/10.1007/s00025-017-0671-y | es_ES |
dc.description.references | N. Doüvelmeyer and W. Wenzel, A characterization of ordered sets and lattices via betweenness relations, Results Math. 46 (2004), 237-250. https://doi.org/10.1007/BF03322885 | es_ES |
dc.description.references | P. C. Fishburn, Betweenness, orders and interval graphs, J. Pure and Appl. Alg. 1 (1971), 159-178. https://doi.org/10.1016/0022-4049(71)90016-8 | es_ES |
dc.description.references | J. Hedlíková and T. Katrinák, On a characterization of lattices by the betweenness relation- on a problem of M. Kolibiar, Algebra Universalis 28 (1991), 389-400. https://doi.org/10.1007/BF01191088 | es_ES |
dc.description.references | E. V. Huntington, A new set of postulates for betweenness, with proof of complete independence, Trans. Amer. Math. Soc. 26 (1924), 257-282. https://doi.org/10.1090/S0002-9947-1924-1501278-0 | es_ES |
dc.description.references | E. V. Huntington and J. R. Kline, Sets of independent postulates for betweenness, Trans. Amer. Math. Soc. 18 (1917), 301-325. https://doi.org/10.1090/S0002-9947-1917-1501071-5 | es_ES |
dc.description.references | R. Mendris and P. Zlatoš, Axiomatization and undecidability results for metrizable betweenness relations, Proc. Amer. Math. Soc. 123 (1995), 873-882. https://doi.org/10.1090/S0002-9939-1995-1219728-7 | es_ES |
dc.description.references | M. Moszyńska, Theory of equidistance and betweenness relations in regular metric spaces, Fund. Math. 96 (1977), 17-29. https://doi.org/10.4064/fm-96-1-17-29 | es_ES |
dc.description.references | S. B. Nadler Jr., Continuum Theory: An Introduction, Marcel Dekker, New York (1992). | es_ES |
dc.description.references | M. Pasch, Vorlesungen uber Neuere Geometrie, Teubner, Leipzig, (1882). | es_ES |
dc.description.references | E. Pitcher and M. Smiley, Transitivities of betweenness, Trans. Amer. Math. Soc. 52 (1942), 95-114. https://doi.org/10.1090/S0002-9947-1942-0007099-3 | es_ES |
dc.description.references | M. Ploščica, On a characterization of distributive lattices by the betweenness relation, Algebra Universalis 35 (1996), 249-255. https://doi.org/10.1007/BF01195499 | es_ES |
dc.description.references | M. Sholander, Trees, lattices, order, and betweenness, Proc. Amer. Math. Soc. 3 (1952), 369-381. https://doi.org/10.1090/S0002-9939-1952-0048405-5 | es_ES |
dc.description.references | M. Smiley, A comparison of algebraic, metric, and lattice betweenness, Bull. Amer. Math. Soc. 49 (1943), 246-252. https://doi.org/10.1090/S0002-9904-1943-07888-3 | es_ES |
dc.description.references | J. Šimko, Metrizable and R-metrizable betweenness spaces, Proc. Amer. Math. Soc. 127 (1999), 323-325. https://doi.org/10.1090/S0002-9939-99-04515-3 | es_ES |
dc.description.references | J. K. Truss, Betweenness relations and cycle-free partial orders, Math. Proc. Cambridge Philos. Soc. 119 (1996), 631-643. https://doi.org/10.1017/S0305004100074478 | es_ES |
dc.description.references | A. Wald, Axiomatik des Zwischenbegriffesin metrischen Raumen, Math. Ann. 104 (1931), 476-484. https://doi.org/10.1007/BF01457952 | es_ES |