Uniformly refinable maps

• Macías, Sergio ^[1]
  1. [1] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 24, Nº. 1, 2023, págs. 59-81
• Idioma: inglés
• DOI: 10.4995/agt.2023.17345
• Enlaces
  • Texto completo
• Resumen
  • español

    Introducimos la noción de función uniformemente refinable para espacios compactos y de Hausdorff, como una generalización de las funciones refinables originalmente definidas para continuos  métricos por Jo Ford (Heath) y Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.

  • English

    We introduce the notion of uniformly refinable map for compact, Hausdorff spaces, as a generalization of refinable maps originallydefined for metric continua by Jo Ford (Heath) and Jack W. Rogers, Jr., Refinable maps, Colloq. Math., 39 (1978), 263-269.

• Referencias bibliográficas
  • F. Barragán, Induced maps on n-fold symmetric products suspensions, Topology Appl. 158 (2011), 1192-1205. https://doi.org/10.1016/j.topol.2011.04.006
  • R. L. Carlisle, Monotone Maps and ε-Maps Between Graphs, Ph. D. Dissertation, Emory University, 1972.
  • D. Cichon, P. Krupski and K. Omiljanowski, Refinable and monotone maps revisited, Topology Appl. 155 (2008), 207-212. https://doi.org/10.1016/j.topol.2007.09.012
  • R. Engelking, General Topology, Sigma Ser. Pure Math. 6, Heldermann, Berlin, 1989.
  • J. Ford (Heath) and J. W. Rogers, Jr., Refinable maps, Colloq. Math. 39 (1978), 263-269. https://doi.org/10.4064/cm-39-2-263-269
  • E. E. Grace, Refinable graphs are near homeomorphisms, Topology Proc. 2 (1977), 139-149.
  • H. Hosokawa, Aposydesis and coherence of continua under refinable maps, Tsukuba J. Math. 7 (1983), 367-372. https://doi.org/10.21099/tkbjm/1496159832
  • H. Hosokawa, A restriction of a refinable mapping, Bull. Tokyo Gakugei Univ. (4) 43 (1991), 1-4.
  • F. B. Jones, Concerning non-aposyndetic continua, Amer. J. Math. 70 (1948), 403-413. https://doi.org/10.2307/2372339
  • F. B. Jones, Concerning aposyndetic and non-aposyndetic continua, Bull. Amer. Math. Soc. 58 (1952), 137-151. https://doi.org/10.1090/S0002-9904-1952-09582-3
  • H. Kato, Concerning a property of J. L. Kelley and refinable maps, Math. Japan. 31 (1986), 711-719.
  • K. Kuratowski, Topology, Vol. 2, English transl., Academic Press, New York; PWN, Warsaw, 1968.
  • S. Macías, Topics on Continua, 2nd Edition, Springer-Cham, 2018. https://doi.org/10.1007/978-3-319-90902-8
  • S. Macías, Set Function T: An Account on F. B. Jones' Contributions to Topology, Developments in Mathematics 67, Springer, 2021. https://doi.org/10.1007/978-3-030-65081-0
  • J. M. Martínez-Montejano, Mutual aposyndesis of symmetric products, Topology Proc. 24 (1999), 203-213.
  • A. McCluskey and B. McMaster, Undergraduate Topology, Oxford University Press, 2014.
  • E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. https://doi.org/10.1090/S0002-9947-1951-0042109-4
  • A. K. Misra, A note on arcs in hyperspaces, Acta Math. Hung. 45 (1985), 285-288. https://doi.org/10.1007/BF01957022
  • S. Mrówka, On the convergence of nets of sets, Fund. Math. 45 (1958), 237-246. https://doi.org/10.4064/fm-45-1-237-246
  • R. H. Songenfrey, Concerning continua irreducible about npoints, American J. Math. 68 (1946), 667-671. https://doi.org/10.2307/2371790