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On setwise betweenness

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On setwise betweenness

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Shakir, QR. (2023). On setwise betweenness. Applied General Topology. 24(1):115-123. https://doi.org/10.4995/agt.2023.18061

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Título: On setwise betweenness
Autor: Shakir, Qays Rashid
Fecha difusión:
Resumen:
[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 ...[+]
Palabras clave: Betweenness relation , Road system , Hyperspace
Derechos de uso: Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
Fuente:
Applied General Topology. (issn: 1576-9402 ) (eissn: 1989-4147 )
DOI: 10.4995/agt.2023.18061
Editorial:
Universitat Politècnica de València
Versión del editor: https://doi.org/10.4995/agt.2023.18061
Tipo: Artículo

References

P. Bankston, Road systems and betweenness, Bull. Math. Sci. 3 (2013), 389-408. https://doi.org/10.1007/s13373-013-0040-4

P. Bankston, When Hausdorff continua have no gaps, Topology Proc. 44 (2014), 177-188.

P. Bankston, The antisymmetry betweenness axiom and Hausdorff continua, Topology Proc. 45 (2015), 189-215. [+]
P. Bankston, Road systems and betweenness, Bull. Math. Sci. 3 (2013), 389-408. https://doi.org/10.1007/s13373-013-0040-4

P. Bankston, When Hausdorff continua have no gaps, Topology Proc. 44 (2014), 177-188.

P. Bankston, The antisymmetry betweenness axiom and Hausdorff continua, Topology Proc. 45 (2015), 189-215.

P. Bankston, Topological betweenness relations, Presentation, Oxford Topology Seminar, (2012).

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

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

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

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

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

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

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

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

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

S. B. Nadler Jr., Continuum Theory: An Introduction, Marcel Dekker, New York (1992).

M. Pasch, Vorlesungen uber Neuere Geometrie, Teubner, Leipzig, (1882).

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

M. Ploščica, On a characterization of distributive lattices by the betweenness relation, Algebra Universalis 35 (1996), 249-255. https://doi.org/10.1007/BF01195499

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

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

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

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

A. Wald, Axiomatik des Zwischenbegriffesin metrischen Raumen, Math. Ann. 104 (1931), 476-484. https://doi.org/10.1007/BF01457952

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