Ir al contenido

Documat

Una introducción a los continuos homogéneos

    1. [1] Universidad Nacional Autónoma de México

      Universidad Nacional Autónoma de México

      México

  • Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 29, Nº. 2, 2011 (Ejemplar dedicado a: Revista Integración), págs. 109-126
  • Idioma: español
  • Títulos paralelos:
    • An introduction to homogeneous continua
  • Enlaces
  • Resumen
    • español

      Un continuo es un espacio métrico, compacto y conexo. Un continuo X es homogéneo si para cualesquiera dos de sus puntos x1 y x2 de X, existe un homeomorfismo h: X -> X tal que h(x1) = x2. Presentaremos un poco de historia, ejemplos y propiedades de este tipo de continuos. Daremos una demostración del Teorema de descomposición aposindética de Jones.

    • English

      A continuum is a compact, connected, metric space. A continuum X is homogeneous provided that for each pair of points x1 and x2 of X, there exists a homeomorphism h: X->X such that h(x1) = x2. We present a bit of history, examples and properties of this kind of continua. We give a proof of Jones's Aposyndetic Decomposition Theorem.

  • Referencias bibliográficas
    • Citas [1] Anderson R.D., “A characterization of the universal curve and a proof of its homogeneity”, Ann. Math., 67 (1958), 313-324.
    • [2] Anderson R.D., “One-dimensional continuous curves and a homogeneity theorem”, Ann. Math., 68 (1958), 1-16.
    • [3] Bellamy D.P. and Lum L., “The cyclic connectivity of homogeneous arcwise connected continua”, Trans. Amer. Math. Soc., 266 (1981), 389-396.
    • [4] Bing R.H., “A homogeneous indecomposable plane continuum”, Duke Math. J., 15 (1948), 729-742.
    • [5] Bing R.H., “Snake-like continua”, Duke Math. J., 18 (1951), 653-663.
    • [6] Bing R.H., “Concerning hereditarily indecomposable continua”, Pacific J. Math., 1 (1951), 43-51.
    • [7] Bing R.H., “Each homogeneous nondegenerate chainable continuum is a pseudo-arc”, Proc. Amer. Math. Soc., 10 (1959), 345-346.
    • [8] Bing R.H., “A simple closed curve is the only homogeneous bounded homogeneous plane continuum that contains an arc”, Canad. J. Math.,...
    • [9] Bing R.H. and Jones F.B., “Another homogeneous plane continuum”, Trans. Amer. Math. Soc., 90 (1959), 171-192.
    • [10] Case J.H., “Another 1-dimensional homogeneous continuum which contains an arc”, Pacific J. Math., 11 (1961), 455-469.
    • [11] Charatonik J.J., “History of continuum theory”, en Handbook of the history of general topology Vol. 2 (C. E. Aull y R. Lowen, editores),...
    • [12] Choquet G., “Prolongement d’homeomorphies. Ensembles topologiquement Charactérisation topologique individuelle des ensembles fermés totalement...
    • [13] Cohen H.J., “Some results concerning homogeneous plane continua”, Duke Math. J., 18 (1951), 467-474.
    • [14] Dantzig D. van, “Ueber topologisch homogene kontinua”, Fund. Math., 15 (1930), 102-125.
    • [15] Effros E.G., “Transformation groups and C∗-algebras”, Ann. Math., (2) 81 (1965), 38-55.
    • [16] Espinoza B. and Macías S., “On the set function R”, Topology Appl., 154 (2007), 2988-2996.
    • [17] Fearnley L., “The pseudo-circle is not homogeneous”, Bull. Amer. Math. Soc., 75 (1969), 554-558.
    • [18] Fernández L. and Macías S., “The set functions T and K and irreducible continua”, Colloq. Math., 121 (2010), 79-91.
    • [19] Hagopian C.L., “Homogeneous plane continua”, Houston J. Math., 1 (1975), 35-41.
    • [20] Hagopian C.L., “A characterization of solenoids”, Pacific J. Math., 68 (1977), 425-435.
    • [21] Jones F.B., “Aposyndetic continua and certain boundary problems”, Amer. J. Math., 63 (1941), 545-553.
    • [22] Jones F.B., “Concerning non-aposyndetic continua”, Amer. J. Math., 70 (1948), 403-413.
    • [23] Jones F.B., “A note on homogeneous plane continua”, Bull. Amer. Math. Soc., 55 (1949), 113-114.
    • [24] Jones F.B., “On a certain type of homogeneous plane continuum”, Proc. Amer. Math. Soc., 6 (1955), 735-740.
    • [25] Jones F.B., “Use of a new technique in homogeneous continua”, Houston J. Math., 1 (1975), 57-61.
    • [26] Kennedy J. and Rogers J.T. Jr., “Orbits of the pseudocircle”, Trans. Amer. Math. Soc., 296 (1986), 327-340.
    • [27] Krasinkiewicz J., “On two theorems of Dyer”, Colloq. Math., 50 (1986), 201-208.
    • [28] Knaster B. and Kuratowski C., “Problèmes”, Fund. Math., 1 (1920), 223.
    • [29] Macías S., “Covering spaces of homogeneous continua”, Topology Appl., 59 (1994), 157-177.
    • [30] Macías S., “Un poco de continuos homogéneos”, en Memorias del XXIX Congreso de Matemáticas de la Sociedad Matemática Mexicana. Aportaciones...
    • [31] Macías S., Topics on continua, Pure and Applied Mathematics Series, Vol. 275, Chapman & Hall/CRC, Taylor & Francis Group, Boca...
    • [32] Macías S., “A class of one-dimensional, nonlocally connected continua for which the set function T is continuous”, Houston J. Math.,...
    • [33] Macías S., “Homogeneous continua for which the set function T is continuous”, Topology Appl., 153 (2006), 3397-3401.
    • [34] Macías S., “A decomposition theorem for a class of continua for which the set function T is continuous”, Colloq. Math., 109 (2007), 163-170.
    • [35] Macías S., “On the continuity of the set function K”, Topology Proc., 34 (2009), 167-173.
    • [36] Macías S., “On continuously irreducible continua”, Topology Appl., 156 (2009), 2357-2363.
    • [37] Macías S., “On the idempotency of the set function T ”, Houston J. Math., 37 (2011), 1297- 1305.
    • [38] Macías S. and Nadler S.B. Jr., “On hereditarily decomposable homogeneous continua”, Topology Proc., 34 (2009), 131-145.
    • [39] Mazurkiewicz S., “Problème 14”, Fund. Math., 2 (1921), 285.
    • [40] Mazurkiewicz S., “Sur les continus homogènes”, Fund. Math., 5 (1924), 137-146.
    • [41] McCord M.C., “Inverse limit sequences with covering maps”, Trans. Amer. Math. Soc., 114 (1965), 197-209.
    • [42] Minc P. and Rogers J.T. Jr., “Some new examples of homogeneous curves”, Topology Proc., 10 (1985), 347-356.
    • [43] Moise E.E., “An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua”, Trans. Amer. Math. Soc.,...
    • [44] Moise E.E., “A note on the pseudo-arc”, Trans. Amer. Math. Soc., 67 (1949), 57-58.
    • [45] Nadler S.B. Jr., Continuum Theory, An Introduction, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 158, Marcel Dekker,...
    • [46] Rogers J.T. Jr., “The pseudo-circle is not homogeneous”, Trans. Amer. Math. Soc., 148 (1970), 417-428.
    • [47] Rogers J.T. Jr., “An aposyndetic homogeneous curve that is not locally connected”, Houston J. Math., 9 (1983), 433-440.
    • [48] Rogers J.T. Jr., “Orbits of higher-dimensional hereditarily indecomposable continua”, Proc. Amer. Math. Soc., 95 (1985), 483-486.
    • [49] Rogers J.T. Jr., “Higher dimensional aposyndetic decompositions”, Proc. Amer. Math. Soc., 131 (2003), 3285-3288.
    • [50] Sierpiński W., “Sur une propiété topologique des ensembles dénombrables denses en soi”, Fund. Math., 1 (1920), 11-16.
    • [51] Waraszkiewicz Z., “Sur les courbes planes topologiquement homogènes”, C. R. Acad. Sci. Paris, 204 (1937), 1388-1390.
Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno