Pellicer–Covarrubias, Cells in hyperspaces, Topology Appl. of non-refinable mappings whose induced mappings are near-homeomorphisms, in. Pellicer, The hyperspaces C ( p, X ), Topol. For a metric continuum X we denote by 2X and C(X) the hyperspaces of all. Nadler, Jr., Continuum Theory: An introduction, Monographs and Textbooks in Pure and Applied Mathematics, 158, Marcel Dekker, Inc., New York and Basel, 1992. Nadler, Jr., Hyperspaces of Sets: A Text with Research Questions, Monographs and Textbooks in Pure and Applied Mathematics, 49, Marcel Dekker, Inc., New York and Basel, 1978. Martínez de la Vega, Dimension of n-fold hyperspaces of graphs, Houston J. Nadler, Jr., Hyperspaces, Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, New York. Eberhart, Intervals of continua which are Hilbert Cubes, Proc. Toalá–Enríquez, Uniqueness of the hyperspaces C ( p, X ) in the class of trees, Topology Appl. We also want to thank Professors Fernando Macías Romero and David Herrera Carrasco for asking the questions wich motivated us to write down this paper. homeomorphism h of E onto E so that h(Xn) Yn in particular. The authors wish to thank Eli Vanney Roblero and Rosemberg Toalá for the fruitful discussions. hyperspaces of compacta X for which D(X) > uniformly are also obtained. In particular, this notion is invariant under affine homeomorphism, i.e., if. Introduction, North-Holland and Elsevier Sci. Observe that the definition of rint K has been stated in affine topological terms. Infinite-dimensional Topology: Prerequisites and Monotone decompositions of irreducible continua,ĭissertationes Math. 49, MarcelĬontinuum Theory: An Introduction, Pure andĪpplied Mathematics Series, Vol. Questions, Pure and Applied Mathematics Series, Vol. Hyperspaces of Sets - A Text with Research On homeomorphisms of the Sierpinski curve, Recent Advances, Pure and Applied Mathematics Series 216, MarcelĪn atriodic tree-like continuum with positive span, Topology, Allyn and Bacon, Inc., Boston, 1966. 71 (1951), 267-273.Īn atriodic tree-like continuum with positive span which admitsĪ monotone mapping to a chainable continuum, Higher-dimensional hereditarily indecomposable continua, Theory, Lecture Notes in Pure and Applied Mathematics 230, Marcelĭekker, Inc., New York and Basel, 2002, 33-49. Product, orbit, property of Kelley, simple closed curve, simpleĬontinua with unique hyperspace, Continuum Hilbert cube, homogeneous, 1/2-homogeneous,ġ/ n-homogeneous, hyperspace, layers (tranches), locallyĬonnected, n-cell, n-fold hyperspace, n-fold symmetric Arc, arc-like, atriodic, chainable,Ĭircle-like, connected im kleinen, continuum, finest monotone map, We do not know whether an arc and a simple closed curve are Nondegenerate atriodic continuum, and if C( X) isġ/2-homogeneous, then X is an arc or a simple closedĬurve. Shown that if X is a locally connected continuum or a We are interestedġ/2-homogeneous, meaning that there are exactly two orbits for theĪction of the group of homeomorphisms of C( X) onto 04510,Į-mail: Let C( X) be the hyperspace of all subcontinua of a Box 6310, Morgantown, WV 26506-6310, USAĭepartamento de Matemáticas, Facultad de Ciencias,Ĭircuito Exterior, Ciudad Universitaria, México, D. We also apply our theory to give a full description of admissible period sets for. Box 6310,Į-mail: Pellicer-Covarrubias, Department of Mathematics, construct an almost totally minimal homeomorphism of the Cantor set. HYPERSPACES WITH EXACTLY TWO ORBITS Sam B. Hyperspaces with exactly two orbits Glasnik Matematicki, Vol.
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