West: 2I is homeomorphic to the Hilbert cube. West: Triangulated infinite-dimensional manifolds. Dranishnikov), Topology and its Applications 80 (1997), 101114. ![]() Compact group actions that raise dimension to infinity (with A. Schori: Topological classification of infinite-dimensional manifolds by homotopy type. Involutions of Hilbert cubes that are hyperspaces of Peano continua, Topology and its Applications, 240 (2018), 238-248. ![]() Henderson: Open subsets of Hilbert space. Henderson: Infinite-dimensional manifolds are open subsets of Hilbert space. Richard Summerhill: Pseudo-boundaries and pseudo-interiors in Euclidean spaces and topological manifolds. homeomorphism h of E onto E so that h(Xn) Yn in particular. Every uniformly continuous homeomorphism f : X Y between metric spaces lifts to a continuous mapping Ff : H(X) H(Y ) of the corresponding hyperspaces. Schori: Hyperspaces of Peano continua are Hilbert cubes (in preparation). hyperspaces of compacta X for which D(X) > uniformly are also obtained. Chapman: All Hilbert cube manifolds are triangulable. Generalizing 1, Proposition 3.1, we claim that always the w-closure of X(X) is. Pelczyński: Estimated extension theorem, homogeneous collections and skeletons and their application to topological classification of linear metric spaces. The map X is w continuous it is a homeomorphism onto its image if X is T0. Barit: Small extensions of small homeomorphisms. Chapman: Extending homeomorphisms to Hilbert cube manifolds. By CldF(X), we denote the space of all closed sets in a space X (including the empty set ) with the Fell topology. Anderson: On sigma-compact subsets of infinite-dimensional spaces. Anderson: On topological infinite deficiency. Anderson: Hilbert space is homeomorphic to the countable infinite product of lines. Pellicer–Covarrubias, Cells in hyperspaces, Topology Appl. Pellicer, The hyperspaces C ( p, X ), Topol. 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. An extremal quasiconformal homeomorphisms in a class of homeomorphisms between two CR 3-manifolds is an one which has the least conformal distortion among this class. ![]() 2, let Cn(X) be the n-fold hyperspace of X consisting of nonempty closed subsets of X with at most n. ![]() Nadler, Jr., Hyperspaces, Fundamentals and recent advances, Monographs and Textbooks in Pure and Applied Mathematics, 216, New York. Request PDF Quotients of n-fold hyperspaces Given a continuum X and an integer n. Eberhart, Intervals of continua which are Hilbert Cubes, Proc. We determine the homeomorphism type of the hyperspace of positively curved Cinfty convex bodies in mathbb Rn, and derive various properties of its. 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. The authors wish to thank Eli Vanney Roblero and Rosemberg Toalá for the fruitful discussions.
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