Ir al contenido

Documat


Continua whose hyperspace of subcontinua is infinite dimensional and a cone

  • Sergio Macías [1] ; Sam B. Nadler Jr.
    1. [1] Instituto de Matemáticas, Circuito Exterior, Ciudad Universitaria CDMX, C.P. 04510, México
  • Localización: Extracta mathematicae, ISSN-e 0213-8743, Vol. 38, Nº 2, 2023, págs. 205-219
  • Idioma: inglés
  • DOI: 10.17398/2605-5686.38.2.205
  • Enlaces
  • Resumen
    • We determine several classes of continua whose hyperspaces of subcontinua are infinite dimensional and homeomorphic to cones over (usually) other continuum. In particular, we obtain many Peano continua with such a property.

  • Referencias bibliográficas
    • 1]R.H. Bing,Partitioning a set,Bull. Amer. Math. Soc.55(1949), 1101 – 1110.
    • [2]T.A. Chapman,On the structure of Hilbert cube manifolds,CompositioMath.24(1972), 329 – 353.
    • [3]T.A. Chapman,“ Lectures on Hilbert Cube Manifolds ”, Rgional ConferenceSeries in Mathematics, no. 28, AMS, Providence, RI, 1976
    • [4]W.J. Charatonik, A. Dilks,On self-homeomorphic spaces,TopologyAppl.55(1994), 215 – 238.
    • [5]D.W. Curtis, R.M. Schori,Hyperspaces which characterize simplehomotopy type,Geneneral Topology and Appl.6(1976), 153 – 165.
    • [6]D.W. Curtis, R.M. Schori,Hyperspaces of Peano continua are Hilbertcubes,Fund. Math.101(1978), 19 – 38.
    • [7]R. Duda,On the hyperspace of subcontinua of a finite graph, I,Fund. Math.62(1968), 265 – 286.
    • [8]C. Eberhart, S.B. Nadler, Jr.,Hyperspaces of cones and fans,Proc.Amer. Math. Soc.77(1979), 279 – 288.
    • [9]M. Handel,On certain sums of Hilbert cubes,Geneneral Topology and Appl.9(1978), 19 – 28.
    • [10]W. Hurewicz, H. Wallman,“ Dimension Theory ”, Princeton UniversityPress, Princeton, NJ, 1941.
    • [11]A. Illanes, M. de J. L ́opez,Hyperspaces homeomorphic to cones, II,Topology Appl.126(2002), 377 – 391.
    • [12]A. Illanes, V. Mart ́ınez-de-la-Vega, D. Michalik,n-fold hyper-spaces as cones,Rocky Mountain J. Math.49(2019), 2185 – 2203.
    • [13]A. Illanes, S.B. Nadler, Jr.,“ Hyperspaces: Fundamentals andRecent Advances ”, Monogr. Textbooks Pure Appl. Math., 216,...
    • [14]M. de J. L ́opez,Hyperspaces homeomorphic to cones,Topology Appl.126(3) (2002), 361 – 375.
    • [15]S. Mac ́ıas,Hyperspaces and cones,Proc. Amer. Math. Soc.125(1997),3069 – 3073.
    • [16]S. Mac ́ıas,Fans whose hyperspaces are cones,Topology Proc.27(2003),217 – 222.
    • [17]S. Mac ́ıas,“ Topics on Continua, 2nd Ed.”, Springer, Cham, 2018.
    • [18]S. Mac ́ıas, S.B. Nadler, Jr.n-fold hyperspaces, cones and products,Topology Proc.26(2001/02/2002), 255 – 270.
    • [19]S. Mac ́ıas, S.B. Nadler, Jr.,Fans whose hyperspace of subcontinua arecones,Topology Appl.126(2002), 29 – 36.
    • [20]E.E. Moise,Grille decomposition and convexification theorems for com-pact metric locally connected continua,Bull. Amer. Math. Soc.55(1949),1111...
    • [21]S.B. Nadler, Jr.,A characterization of locally connected continua byhyperspace retractions,Proc. Amer. Math. Soc.67(1977), 167...
    • [22]S.B. Nadler, Jr.,“ Hyperspaces of Sets ”, Monogr. Textbooks Pure Appl.Math., Vol. 49, Marcel Dekker, Inc., New York-Basel, 1978. (Reprinted...
    • [23]S.B. Nadler, Jr.,“ Continuum Theory: An Introduction ”, Monogr. Text-books Pure Appl. Math., 158, Marcel Dekker, Inc., New York, 1992.

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno