Please see Wikipedias template documentation for further citation fields that may be required. Unsolved and Partially Solved Questions of 82. 1978, Hyperspaces of sets : a text with research questions / Sam B. Wrinkles Folds Proof of the Main Theorem Exercises 80. Smoothness in Hyperspaces $R^3$-Sets Spaces of Finite Subsets Admissibility Maps Preserving Hyperspace Contractibility More on Kelley's Property Exercises References XIV. More on Contractibility of HyperspacesĬontractibility vs. Retractions between HyperspacesĮxercises References XIII. Special Types of Maps between HyperspacesĮxercises 76. Proof that $H_d$ Is a Metric A Results about Metrizability of $\mathrm(X)$ for $1$-Dimensional Continua $X$ References XII. Topological Invariance Specified Hyperspaces Exercises 2. Nadler, Jr.: Hyperspaces, Fundamentals and Recent Advances Schori and West proved that K() is homeomorphic with the Hilbert cube, while Hohti showed that K() is not bi-Lipschitz equivalent with a variety of metric Hilbert cubes.Alejandro Illanes and Sam B. In this paper we survey the theory of some of the structures that have been defined on sets of subsets, and illustrate the way motivation has come from. By way of contrast, the hyperspace K() of the unit interval contains a bi-Lipschitz copy of a certain self-similar doubling series-parallel graph studied by Laakso, Lang-Plaut, and Lee-Mendel-Naor, and consequently admits no bi-Lipschitz embedding into any uniformly convex Banach space. How to cite abstract = $ in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. Schori and West proved that K() is homeomorphic with the Hilbert cube, while Hohti showed that K() is not bi-Lipschitz equivalent with a variety of metric Hilbert cubes. The proof of Theorem E will be given in the last section. The proofs of Theorems C and D are similar in form and will be presented together in Sections 2-5. By way of contrast, the hyperspace K() of the unit interval contains a bi-Lipschitz copy of a certain self-similar doubling series-parallel graph studied by Laakso, Lang-Plaut, and Lee-Mendel-Naor, and consequently admits no bi-Lipschitz embedding into any uniformly convex Banach space. Further results on hyperspaces of finite sets homeomorphic to 12 have been given in 6. In this paper we study the topological structure of certain hyperspaces of convex subsets of. Let n be a natural number equal or greater than 2. We focus our attention on the hyperspace. If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ℝ n 1 in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. In this paper we study the topological structure of certain hyperspaces of convex subsets of constant width, equipped with the Hausdorff metric topology. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. C(X)-coselection spaces and Z-sets in hyperspaces. In this paper we study the hyperspace of all nonempty closed totally disconnected subsets of a space, equipped with the Vietoris topology. Bi-Lipschitz embeddings of hyperspaces of compact sets Martinez-Montejano, Jorge M., Results on hyperspaces (2004).
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